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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
Journal Article
ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 07/2017, Volume 23, Issue 3, pp. 1145 - 1177
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 $$\begin{aligned} \text {find } (U,\lambda )\in H^1_0(\Omega )\times {\mathbb {R}}\text { such that }... 
35J20 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35Q55 | Mathematics | 35C08 | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SUPERCRITICAL NLS | MORSE INDEX | STANDING WAVES | UNBOUNDED-DOMAINS | ORBITAL STABILITY | CRITICAL-POINTS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2018, Volume 370, Issue 10, pp. 7149 - 7179
We prove that the planar hexagonal honeycomb is asymptotically optimal for a large class of optimal partition problems, in which the cells are assumed to be... 
Logarithmic capacity | Discrete faber-krahn inequality | Cheeger constant | Honeycomb conjecture | Optimal partitions | MATHEMATICS | EIGENVALUES | logarithmic capacity | discrete Faber-Krahn inequality | INEQUALITY | honeycomb conjecture | N-GONS | Analysis of PDEs | Mathematics
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 12/2014, Volume 39, Issue 12, pp. 2284 - 2313
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 03/2010, Volume 63, Issue 3, pp. 267 - 302
For the positive solutions of the Gross–Pitaevskii system $$ \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
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
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2/2013, Volume 207, Issue 2, pp. 583 - 609
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
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
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
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
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
Journal Article
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
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 12, pp. 2865 - 2924
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
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 06/2014, Volume 34, Issue 6, pp. 2669 - 2691
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 1/2005, Volume 54, Issue 3, pp. 779 - 815
Journal Article
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