Singularly perturbed nonlinear Dirichlet problems involving critical growth

DOI10.1007/s00526-012-0511-6zbMath1270.35042OpenAlexW2090708750MaRDI QIDQ1949420

Jaeyoung Byeon, Jian Jun Zhang, Wen Ming Zou

Publication date: 7 May 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-012-0511-6

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Variational methods applied to PDEs (35A15) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Semilinear elliptic equations (35J61)

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Cites Work

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• Nonlinear scalar field equations. I: Existence of a ground state
• Singularly perturbed nonlinear Neumann problems with a general nonlinearity
• On least energy solutions to a semilinear elliptic equation in a strip
• Symmetry and monotonicity of least energy solutions
• Existence of solitary waves in higher dimensions
• Remarks on the Schrödinger operator with singular complex potentials
• On spike solutions of singularly perturbed semilinear Dirichlet problem
• Multi-peak bound states for nonlinear Schrödinger equations
• Standing waves with a critical frequency for nonlinear Schrödinger equations. II.
• Elliptic partial differential equations of second order
• Elliptic problems with critical exponents and Hardy potentials.
• On the location of the peaks of least-energy solutions to semilinear Dirichlet problems with critical growth
• Local mountain passes for semilinear elliptic problems in unbounded domains
• Minimax theorems
• On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: Intermediate solutions
• Solutions with multiple spike patterns for an elliptic system
• Mountain pass solutions for singularly perturbed nonlinear Dirichlet problems
• Standing waves for nonlinear Schrödinger equations with a general nonlinearity
• Variational approach to bifurcation from infinity for nonlinear elliptic problems
• The set of positive solutions of semilinear equations in large balls
• A BERESTYCKI–LIONS THEOREM REVISITED
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Singularly perturbed nonlinear Dirichlet problems with a general nonlinearity
• The Effect of the Domain Geometry in Singular Perturbation Problems
• Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting
• A remark on least energy solutions in $\mathbf {R}^N$
• On the location and profile of spike‐layer solutions to singularly perturbed semilinear dirichlet problems
• On the role of distance function in some singular perturbation problems
• Local mountain-pass for a class of elliptic problems in \(\mathbb R^N\) involving critical growth

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