Communications on Pure and Applied Mathematics, ISSN 0010-3640, 12/2019, Volume 72, Issue 12, pp. 2578 - 2620

This paper describes the structure of the nodal set of segregation profiles arising in the singular limit of planar, stationary, reaction‐diffusion systems...

Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Journal of Mathematical Biology, ISSN 0303-6812, 5/2018, Volume 76, Issue 6, pp. 1357 - 1386

We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the...

Secondary 35P15 | Periodic environments | 92D25 | Mathematical and Computational Biology | Survival threshold | Mathematics | 47A75 | Applications of Mathematics | Primary 35R11 | Spectral fractional Laplacian | Reflecting barriers | DIFFUSIVE LOGISTIC EQUATIONS | BOUNDARY-CONDITIONS | DISRUPTED ENVIRONMENTS | ANOMALOUS DIFFUSION | MODELS | SPECIES PERSISTENCE | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | FRONT DYNAMICS | WEIGHT | POPULATION-DYNAMICS | LEVY | Eigenvalues | Boundary value problems | Research | Mathematical research | Laplacian operator | Diffusion | Survival | Dispersal | Optimization | Eigen values

Secondary 35P15 | Periodic environments | 92D25 | Mathematical and Computational Biology | Survival threshold | Mathematics | 47A75 | Applications of Mathematics | Primary 35R11 | Spectral fractional Laplacian | Reflecting barriers | DIFFUSIVE LOGISTIC EQUATIONS | BOUNDARY-CONDITIONS | DISRUPTED ENVIRONMENTS | ANOMALOUS DIFFUSION | MODELS | SPECIES PERSISTENCE | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | FRONT DYNAMICS | WEIGHT | POPULATION-DYNAMICS | LEVY | Eigenvalues | Boundary value problems | Research | Mathematical research | Laplacian operator | Diffusion | Survival | Dispersal | Optimization | Eigen values

Journal Article

ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 07/2017, Volume 23, Issue 3, pp. 1145 - 1177

We search for non-constant normalized solutions to the semilinear elliptic system {-v Delta v(i) + g(i) (v(j)(2))v(i) =lambda(i)v(i,) v(i) > 0 in Omega partial...

Singularly perturbed problems | Normalized solutions to semilinear elliptic systems | Multi-population differential games | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | FREE-BOUNDARIES | HOLDER BOUNDS | normalized solutions to semilinear elliptic systems | multi-population differential games | BEHAVIOR | POPULATIONS | STRONGLY COMPETING SYSTEMS | MODELS | MASS | ELLIPTIC-SYSTEMS | DOMAINS | AUTOMATION & CONTROL SYSTEMS | Bifurcations | Populations | Variational methods | Game theory | Differential games

Singularly perturbed problems | Normalized solutions to semilinear elliptic systems | Multi-population differential games | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | FREE-BOUNDARIES | HOLDER BOUNDS | normalized solutions to semilinear elliptic systems | multi-population differential games | BEHAVIOR | POPULATIONS | STRONGLY COMPETING SYSTEMS | MODELS | MASS | ELLIPTIC-SYSTEMS | DOMAINS | AUTOMATION & CONTROL SYSTEMS | Bifurcations | Populations | Variational methods | Game theory | Differential games

Journal Article

Journal de Mathématiques Pures et Appliquées, ISSN 0021-7824, 03/2020, Volume 135, pp. 256 - 283

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 10/2017, Volume 56, Issue 5, pp. 1 - 27

Given $$\rho >0$$ ρ > 0 , we study the elliptic problem $$\begin{aligned} \text {find } (U,\lambda )\in H^1_0(\Omega )\times {\mathbb {R}}\text { such that }...

35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35Q55 | Mathematics | 35C08 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SUPERCRITICAL NLS | MORSE INDEX | STANDING WAVES | UNBOUNDED-DOMAINS | ORBITAL STABILITY | CRITICAL-POINTS

35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35Q55 | Mathematics | 35C08 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SUPERCRITICAL NLS | MORSE INDEX | STANDING WAVES | UNBOUNDED-DOMAINS | ORBITAL STABILITY | CRITICAL-POINTS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 7149 - 7179

We prove that the planar hexagonal honeycomb is asymptotically optimal for a large class of optimal partition problems, in which the cells are assumed to be...

Logarithmic capacity | Discrete faber-krahn inequality | Cheeger constant | Honeycomb conjecture | Optimal partitions | MATHEMATICS | EIGENVALUES | logarithmic capacity | discrete Faber-Krahn inequality | INEQUALITY | honeycomb conjecture | N-GONS | Analysis of PDEs | Mathematics

Logarithmic capacity | Discrete faber-krahn inequality | Cheeger constant | Honeycomb conjecture | Optimal partitions | MATHEMATICS | EIGENVALUES | logarithmic capacity | discrete Faber-Krahn inequality | INEQUALITY | honeycomb conjecture | N-GONS | Analysis of PDEs | Mathematics

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 12/2014, Volume 39, Issue 12, pp. 2284 - 2313

We consider a system of differential equations with nonlinear Steklov boundary conditions, related to the fractional problem where u = (u 1 ,..., u k ),...

Optimal regularity of limiting profiles | Primary: 35J65 | Secondary: 35B40, 35R11, 92D25 | Singular perturbations | Blow-up analysis | Spatial segregation | Monotonicity formulae | OBSTACLE PROBLEM | MATHEMATICS, APPLIED | FREE-BOUNDARIES | EQUATIONS | LAPLACIAN | MATHEMATICS | REGULARITY | ELLIPTIC-SYSTEMS | CONTINUATION | Partial differential equations | Diffusion | Competition | Images | Differential equations | Density | Regularity | Optimization | Constraining

Optimal regularity of limiting profiles | Primary: 35J65 | Secondary: 35B40, 35R11, 92D25 | Singular perturbations | Blow-up analysis | Spatial segregation | Monotonicity formulae | OBSTACLE PROBLEM | MATHEMATICS, APPLIED | FREE-BOUNDARIES | EQUATIONS | LAPLACIAN | MATHEMATICS | REGULARITY | ELLIPTIC-SYSTEMS | CONTINUATION | Partial differential equations | Diffusion | Competition | Images | Differential equations | Density | Regularity | Optimization | Constraining

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 03/2010, Volume 63, Issue 3, pp. 267 - 302

For the positive solutions of the Gross–Pitaevskii system $$ \cases {- \Delta u_{\beta} + \lambda_{\beta}u_{\beta} = \omega_{1}u{3 \over \beta} - \beta...

MATHEMATICS | PHASES | MATHEMATICS, APPLIED | WAVES | FREE-BOUNDARIES | SPATIAL SEGREGATION | EQUATIONS | ELLIPTIC-SYSTEMS

MATHEMATICS | PHASES | MATHEMATICS, APPLIED | WAVES | FREE-BOUNDARIES | SPATIAL SEGREGATION | EQUATIONS | ELLIPTIC-SYSTEMS

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 12/2009, Volume 194, Issue 3, pp. 717 - 741

For the system $$-\Delta U_i+ U_i=U_i^3-\beta U_i\sum_{j\neq i}U_j^2,\quad i=1,\dots,k,$$ (with k ≧ 3), we prove the existence for β large of positive radial...

Solitary Wave | Nodal Domain | Fluid- and Aerodynamics | Einstein Condensate | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | Physics, general | Implicit Function Theorem | Physics | Radial Solution | MATHEMATICS, APPLIED | SYSTEMS | MECHANICS | NONLINEAR SCHRODINGER-EQUATIONS | SOLITARY WAVES

Solitary Wave | Nodal Domain | Fluid- and Aerodynamics | Einstein Condensate | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | Physics, general | Implicit Function Theorem | Physics | Radial Solution | MATHEMATICS, APPLIED | SYSTEMS | MECHANICS | NONLINEAR SCHRODINGER-EQUATIONS | SOLITARY WAVES

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2/2013, Volume 207, Issue 2, pp. 583 - 609

We continue the variational approach to parabolic trajectories introduced in our previous paper (Barutello et al., Entire parabolic trajectories as minimal...

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | ORBITS | MATHEMATICS, APPLIED | MECHANICS | MINIMIZATION | 4-BODY PROBLEM | Anisotropy | Analysis | Phase transformations | Collisions | Homogeneity | Links | Joining | Trajectories | Orbits | Archives | Mathematics - Dynamical Systems

Mechanics | Physics, general | Fluid- and Aerodynamics | Statistical Physics, Dynamical Systems and Complexity | Theoretical, Mathematical and Computational Physics | Physics | EXISTENCE | ORBITS | MATHEMATICS, APPLIED | MECHANICS | MINIMIZATION | 4-BODY PROBLEM | Anisotropy | Analysis | Phase transformations | Collisions | Homogeneity | Links | Joining | Trajectories | Orbits | Archives | Mathematics - Dynamical Systems

Journal Article

Nonlinearity, ISSN 0951-7715, 02/2019, Volume 32, Issue 3, pp. 1044 - 1072

We analyze L-2-normalized solutions of nonlinear Schrodinger systems of Gross-Pitaevskii type, on bounded domains, with homogeneous Dirichlet boundary...

Gross-Pitaevskii systems | critical exponents | solitary waves | orbital stability | constrained critical points | EXISTENCE | MATHEMATICS, APPLIED | HOLDER BOUNDS | POSITIVE SOLUTIONS | EQUATIONS | STANDING WAVES | PHYSICS, MATHEMATICAL | SUPERCRITICAL NLS | CONVERGENCE | GROUND-STATES

Gross-Pitaevskii systems | critical exponents | solitary waves | orbital stability | constrained critical points | EXISTENCE | MATHEMATICS, APPLIED | HOLDER BOUNDS | POSITIVE SOLUTIONS | EQUATIONS | STANDING WAVES | PHYSICS, MATHEMATICAL | SUPERCRITICAL NLS | CONVERGENCE | GROUND-STATES

Journal Article

Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 1/2014, Volume 49, Issue 1, pp. 391 - 429

For the class of anisotropic Kepler problems in $$\mathbb{R }^d\setminus \{0\}$$ with homogeneous potentials, we seek parabolic trajectories having prescribed...

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 74E10 | Mathematics | 37C29 | 37J45 | MATHEMATICS | ORBITS | MATHEMATICS, APPLIED | COLLISION | Anisotropy | Asymptotic properties

Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 74E10 | Mathematics | 37C29 | 37J45 | MATHEMATICS | ORBITS | MATHEMATICS, APPLIED | COLLISION | Anisotropy | Asymptotic properties

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 04/2014, Volume 256, Issue 7, pp. 2526 - 2558

Under the validity of a Landesman–Lazer type condition, we prove the existence of solutions bounded on the real line, together with their first derivatives,...

Critical point theory | Subharmonic solutions to periodic ODEs | Landesman–Lazer conditions | Ambrosetti–Prodi problems | Ambrosetti-Prodi problems | Landesman-Lazer conditions | MATHEMATICS | RESONANCE | ODES | DIFFERENTIAL-EQUATIONS

Critical point theory | Subharmonic solutions to periodic ODEs | Landesman–Lazer conditions | Ambrosetti–Prodi problems | Ambrosetti-Prodi problems | Landesman-Lazer conditions | MATHEMATICS | RESONANCE | ODES | DIFFERENTIAL-EQUATIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 02/2013, Volume 254, Issue 3, pp. 1529 - 1547

For a C2-functional J defined on a Hilbert space X, we consider the set N={x∈A:projVx∇J(x)=0}, where A⊂X is open and Vx⊂X is a closed linear subspace, possibly...

Critical point theory | Nehari manifold | Singularly perturbed domains | Systems of elliptic PDE | EXISTENCE | DOMAIN SHAPE | STATES | ENERGY | POSITIVE SOLUTIONS | STANDING WAVES | ELLIPTIC SYSTEM | MATHEMATICS | SOLITONS | NONLINEAR EQUATIONS | NEUMANN BOUNDARY-CONDITIONS

Critical point theory | Nehari manifold | Singularly perturbed domains | Systems of elliptic PDE | EXISTENCE | DOMAIN SHAPE | STATES | ENERGY | POSITIVE SOLUTIONS | STANDING WAVES | ELLIPTIC SYSTEM | MATHEMATICS | SOLITONS | NONLINEAR EQUATIONS | NEUMANN BOUNDARY-CONDITIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 10/2015, Volume 259, Issue 7, pp. 3448 - 3489

We show the existence of infinitely many positive solutions, defined on the real line, for the nonlinear scalar ODEu¨+(a+(t)−μa−(t))u3=0, where a is a...

Singularly perturbed problems | Nehari method | Periodic and subharmonic solutions | Natural constraints | MATHEMATICS | EQUATIONS | BOUNDED SOLUTIONS

Singularly perturbed problems | Nehari method | Periodic and subharmonic solutions | Natural constraints | MATHEMATICS | EQUATIONS | BOUNDED SOLUTIONS

Journal Article

16.
Full Text
Existence and Nonexistence of Entire Solutions for Non-Cooperative Cubic Elliptic Systems

Communications in Partial Differential Equations, ISSN 0360-5302, 11/2011, Volume 36, Issue 11, pp. 1988 - 2010

In this article we deal with the cubic Schrödinger system where β = (β i, j ) ij is a symmetric matrix with real coefficients and β ii ≥ 0 for every...

Copositive matrices | Secondary 35B08, 35B09, 35B53 | Elliptic systems | Existence and nonexistence results | Positive solutions | Variational methods | Primary 35J50 | MATHEMATICS | MATHEMATICS, APPLIED | R-N | STATES | NONLINEAR SCHRODINGER-EQUATIONS | BOUNDS | Nonlinearity | Schroedinger equation | Partial differential equations | Joints

Copositive matrices | Secondary 35B08, 35B09, 35B53 | Elliptic systems | Existence and nonexistence results | Positive solutions | Variational methods | Primary 35J50 | MATHEMATICS | MATHEMATICS, APPLIED | R-N | STATES | NONLINEAR SCHRODINGER-EQUATIONS | BOUNDS | Nonlinearity | Schroedinger equation | Partial differential equations | Joints

Journal Article

Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 12, pp. 2865 - 2924

For a class of competition-diffusion nonlinear systems involving the square root of the laplacian, including the fractional Gross-Pitaevskii system....

Singular perturbations | Optimal regularity of limiting profiles | Strongly competing systems | Square root of the laplacian | Spatial segregation | OBSTACLE PROBLEM | singular perturbations | MATHEMATICS, APPLIED | FREE-BOUNDARIES | SEGREGATION | optimal regularity of limiting profiles | CONJECTURE | FRACTIONAL LAPLACIAN | MATHEMATICS | REGULARITY | spatial segregation | ELLIPTIC-SYSTEMS | DIFFUSION | strongly competing systems

Singular perturbations | Optimal regularity of limiting profiles | Strongly competing systems | Square root of the laplacian | Spatial segregation | OBSTACLE PROBLEM | singular perturbations | MATHEMATICS, APPLIED | FREE-BOUNDARIES | SEGREGATION | optimal regularity of limiting profiles | CONJECTURE | FRACTIONAL LAPLACIAN | MATHEMATICS | REGULARITY | spatial segregation | ELLIPTIC-SYSTEMS | DIFFUSION | strongly competing systems

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 12/2015, Volume 35, Issue 12, pp. 6085 - 6112

For the cubic Schrodinger system with trapping potentials in R-N, N <= 3, or in bounded domains, we investigate the existence and the orbital stability of...

Orbital stability | Gross-Pitaevskii systems | Ambrosetti-Prodi type problem | Cooperative and competitive elliptic systems | Constrained critical points | EXISTENCE | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | EQUATIONS | STANDING WAVES | MATHEMATICS | R-N | SYMMETRY | BOUND-STATES | constrained critical points | orbital stability | DOMAINS

Orbital stability | Gross-Pitaevskii systems | Ambrosetti-Prodi type problem | Cooperative and competitive elliptic systems | Constrained critical points | EXISTENCE | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | EQUATIONS | STANDING WAVES | MATHEMATICS | R-N | SYMMETRY | BOUND-STATES | constrained critical points | orbital stability | DOMAINS

Journal Article

Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 06/2014, Volume 34, Issue 6, pp. 2669 - 2691

For a class of competition-diffusion nonlinear systems involving the s-power of the laplacian, s is an element of (0, 1), of the form (-Delta)(s) u(i) =...

Singular perturbations | Optimal regularity of limiting profiles | Fractional laplacian | Strongly competing systems | Spatial segregation | OBSTACLE PROBLEM | MATHEMATICS | singular perturbations | MATHEMATICS, APPLIED | spatial segregation | ELLIPTIC-SYSTEMS | SEGREGATION | optimal regularity of limiting profiles | strongly competing systems

Singular perturbations | Optimal regularity of limiting profiles | Fractional laplacian | Strongly competing systems | Spatial segregation | OBSTACLE PROBLEM | MATHEMATICS | singular perturbations | MATHEMATICS, APPLIED | spatial segregation | ELLIPTIC-SYSTEMS | SEGREGATION | optimal regularity of limiting profiles | strongly competing systems

Journal Article

Indiana University Mathematics Journal, ISSN 0022-2518, 1/2005, Volume 54, Issue 3, pp. 779 - 815

In this paper we study a class of stationary states for reaction-diffusion systems of k ≥ 3 densities having disjoint supports. For a class of segregation...

Ecological competition | Uniqueness | Elliptic equations | Eigenvalues | Mathematics | Convexity | Reaction-diffusion systems | Lagrangian function | Vertices | Differential variability inequalities | Regularity theory | Multiple intersection points | Monotonicity formula | Segregation states | monotonicity formula | regularity theory | POSITIVE SOLUTIONS | EQUATIONS | FREE-BOUNDARY | MODEL | multiple intersection points | COEXISTENCE STATES | STEADY-STATE SOLUTIONS | MATHEMATICS | segregation states | 3-SPECIES COMPETITION SYSTEM | CROSS-DIFFUSION | BIOLOGY

Ecological competition | Uniqueness | Elliptic equations | Eigenvalues | Mathematics | Convexity | Reaction-diffusion systems | Lagrangian function | Vertices | Differential variability inequalities | Regularity theory | Multiple intersection points | Monotonicity formula | Segregation states | monotonicity formula | regularity theory | POSITIVE SOLUTIONS | EQUATIONS | FREE-BOUNDARY | MODEL | multiple intersection points | COEXISTENCE STATES | STEADY-STATE SOLUTIONS | MATHEMATICS | segregation states | 3-SPECIES COMPETITION SYSTEM | CROSS-DIFFUSION | BIOLOGY

Journal Article

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