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Journal of mathematical fluid mechanics, ISSN 1422-6952, 2017, Volume 20, Issue 1, pp. 161 - 187
Journal Article
Archive for rational mechanics and analysis, ISSN 1432-0673, 2019, Volume 235, Issue 1, pp. 405 - 470
We study the existence of patterns (nontrivial, stationary solutions) in the onedimensional Swift-Hohenberg Equation in a directional quenching scenario, that... 
PATTERN-FORMATION | MATHEMATICS, APPLIED | GRAIN-BOUNDARIES | DEFECTS | MECHANICS | INTERFACES | SYSTEMS | ANGLE | VALIDITY | BIFURCATION | Fourier analysis | Orbits | Decomposition | Quenching
Journal Article
Nonlinear dynamics, ISSN 0924-090X, 2019, Volume 97, Issue 1, pp. 571 - 582
This paper presents necessary and sufficient conditions for the existence of bright/dark solitary solutions in the Hodgkin-Huxley model. The second-order... 
Hodgkin-Huxley model | MECHANICS | EXP-FUNCTION | Heteroclinic bifurcation | 35B32 | NEURONS | Generalized differential operator | Solitary solution | 35C08 | DESYNCHRONIZATION | ENGINEERING, MECHANICAL | Operators (mathematics) | Economic models | Broken symmetry | Saddle points | Differential equations | Bifurcations | Trajectories | Symmetry
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 2018, Volume 19, Issue 2, pp. 391 - 412
We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights,... 
Concave-Convex Problem | Positive Solution | Loop Bifurcation | Indefinite Nonlinearity | MATHEMATICS | MATHEMATICS, APPLIED | LOCAL SUPERLINEARITY | FIXED-POINT EQUATIONS
Journal Article
Calculus of variations and partial differential equations, ISSN 1432-0835, 2009, Volume 37, Issue 3-4, pp. 345 - 361
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 2/2019, Volume 58, Issue 1, pp. 1 - 23
In the paper the asymptotic bifurcation of solutions to a parameterized stationary semilinear Schrödinger equation involving a potential of the Kato-Rellich... 
37B30 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35J | 35B32 | 35K | Mathematics
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 2016, Volume 289, Issue 2-3, pp. 332 - 342
We prove a bifurcation and multiplicity result for a critical fractional p‐Laplacian problem that is the analog of the Brézis‐Nirenberg problem for the... 
bifurcation | 58E05 | critical nonlinearity | 35B33 | 35B32 | 35R11 | pseudo‐index | cohomological index | Fractional p‐Laplacian | Bifurcation | Fractional p-Laplacian | Pseudo-index | Cohomological index | Critical nonlinearity | pseudo-index | EIGENVALUE | EXISTENCE | POSITIVE SOLUTIONS | BREZIS-NIRENBERG RESULT | EQUATIONS | MATHEMATICS | ELLIPTIC PROBLEMS | R-N | CRITICAL SOBOLEV EXPONENTS | FUNCTIONALS
Journal Article
ADVANCED NONLINEAR STUDIES, ISSN 1536-1365, 11/2019, Volume 19, Issue 4, pp. 757 - 770
We consider the Henon problem {-Delta u = vertical bar x vertical bar(alpha)u(N+2+2 alpha/N-2-epsilon )in B-1, u > 0 in B-1, u = 0 on partial derivative B-1,... 
Henon Problem | MATHEMATICS | MATHEMATICS, APPLIED | SEMILINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | Bifurcation | DOMAINS | Nonradial Solutions | SYMMETRY-BREAKING
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 1/2017, Volume 108, Issue 1, pp. 71 - 83
We study the solution $${u(r,\rho)}$$ u ( r , ρ ) of the quasilinear elliptic problem $$\begin{cases}... 
Secondary 35C10 | Singular solutions | Intersection number | 35B32 | Mathematics, general | Mathematics | 70K05 | Quasilinear elliptic equation | Radial solutions | Primary 35B05 | MATHEMATICS
Journal Article
Zeitschrift für angewandte Mathematik und Physik, ISSN 1420-9039, 2019, Volume 70, Issue 4, pp. 1 - 13
We study a superlinear and subcritical Kirchhoff-type equation which is variational and depends upon a real parameter $$\lambda $$ λ . The nonlocal term forces... 
Young’s modulus | Engineering | Mathematical Methods in Physics | Nehari Manifold | Variational methods | 35A15 | Kirchhoff | 35B32 | Stiffness | Primary 35A02 | Theoretical and Applied Mechanics | Extremal parameter | Mathematics - Analysis of PDEs
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 11/2017, Volume 290, Issue 16, pp. 2597 - 2611
In this paper, we consider the bifurcation problem for the fractional Laplace equation (−Δ)su=λu+f(λ,x,u)inΩ,u=0inRn∖Ω,where Ω⊂Rn,n>2s(0 bifurcation | Variational methods | 35A15 | 47G20 | fractional Laplacian | 35B32 | integrodifferential operators | OBSTACLE PROBLEM | MATHEMATICS | EIGENVALUES | P-LAPLACIAN | REGULARITY | FREE-BOUNDARY
Journal Article
Communications in partial differential equations, ISSN 1532-4133, 2015, Volume 40, Issue 5, pp. 918 - 956
Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations... 
Network formation | Stability | Weak solutions | Energy dissipation | Bifurcation analysis | MATHEMATICS | MATHEMATICS, APPLIED | 92C42 | MEAN-OSCILLATION | 35B32 | 35K55 | Market analysis | Business incubators | Environmental protection | Partial differential equations | Dynamics | Mathematical analysis | Mathematical models | Conductance | Dynamical systems | Steady state
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 4/2018, Volume 57, Issue 2, pp. 1 - 26
In this paper we establish existence of radial and nonradial solutions to the system $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle -\Delta u_1 =... 
Primary 35J47 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 35B33 | 35B32 | Secondary 35B09 | Mathematics | 35B08 | MATHEMATICS | MATHEMATICS, APPLIED | ELLIPTIC SYSTEM
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 15
This paper investigates the stability of bifurcating steady states of a spatially heterogeneous cooperative system with cross-diffusion. According to the... 
Ordinary Differential Equations | Functional Analysis | 35B35 | Analysis | Difference and Functional Equations | 35B32 | Mathematics, general | spectral analysis | Mathematics | Partial Differential Equations | stability | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | INSTABILITY | MODEL
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 2/2019, Volume 95, Issue 3, pp. 1731 - 1745
A general diffusive population model for interactions of pioneer and climax species subject to the no-flux boundary condition is considered. Local and global... 
Spatial–temporal pattern | Climax species | Classical Mechanics | 35K57 | Engineering | Vibration, Dynamical Systems, Control | 92B05 | 92D25 | Turing bifurcation | 35B32 | Automotive Engineering | Mechanical Engineering | Pioneer species | Diffusion | Hopf bifurcation | MECHANICS | Spatial-temporal pattern | ENGINEERING, MECHANICAL | Analysis | Models | Numerical analysis
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 11/2018, Volume 18, Issue 4, pp. 845 - 862
The purpose of this paper is to study properties of continua (closed connected sets) of nontrivial solutions of non-cooperative elliptic systems considered on... 
Non-cooperative Elliptic Systems | Symmetric Rabinowitz Alternative | Equivariant Degree | Global Symmetry-Breaking Bifurcations | MATHEMATICS | MATHEMATICS, APPLIED | EQUATIONS | BIFURCATION
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 06/2017, Volume 56, Issue 3, p. 1
We consider the stationary Keller-Segel equation {-Lambda v + v = lambda e(v), v > 0 in Omega, partial derivative(nu)v = 0 on partial derivative Omega, where... 
35B32 | 35B05 | 35B40 | 35B25 | 35J25 | 35B09 | MATHEMATICS | RADIAL SOLUTIONS | MATHEMATICS, APPLIED | PERTURBED NEUMANN PROBLEM | STEADY-STATES | CHEMOTAXIS | BEHAVIOR | Analysis of PDEs | Mathematics
Journal Article
Journal of mathematical biology, ISSN 1432-1416, 2018, Volume 78, Issue 3, pp. 655 - 682
Journal Article
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 08/2017, Volume 147, Issue 4, pp. 875 - 894
Positive solutions of a Kirchhoff-type nonlinear elliptic equation with a non-local integral term on a bounded domain in ℝ N , N ⩾ 1, are studied by using... 
35J62 | 35J25 | 2010 Mathematics subject classification: Primary 35J60 | Secondary 35B32 | EXISTENCE | GLOBAL SOLVABILITY | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | MULTIPLICITY | BEHAVIOR | NONTRIVIAL SOLUTIONS | bifurcation theory | UNIQUENESS | Kirchhoff-type equation | MATHEMATICS | positive solution | CRITICAL GROWTH | R-3 | DOMAINS | Eigenvalues | Bifurcation theory | Uniqueness | Eigen values
Journal Article
Journal of mathematical biology, ISSN 0303-6812, 2012, Volume 66, Issue 6, pp. 1241 - 1266
Journal Article
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