Existence and behavior of positive solution for a problem with discontinuous nonlinearity in \({\mathbb{R}}^N\) via a nonsmooth penalization

DOI10.1007/s00033-020-01296-7zbMath1437.35385OpenAlexW3013085866MaRDI QIDQ2175340

Rúbia G. Nascimento, Gelson G. dos Santos, Giovany M. Figueiredo

Publication date: 29 April 2020

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-020-01296-7

zbMATH Keywords

existence of positive solutionsvariational methodssemilinear equation with Laplaciandiscontinuous nonlinearity

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Positive solutions to PDEs (35B09) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (6)

The topological degree methods for the fractional p(·)-Laplacian problems with discontinuous nonlinearities ⋮ Existence and behavior of positive solutions for a class of linearly coupled systems with discontinuous nonlinearities in \(\mathbb{R}^N\) ⋮ Existence of solutions for a class of quasilinear equations with vanishing potentials ⋮ A positive solution for a weighted \(p\)-Laplace equation with Hardy-Sobolev's critical exponent ⋮ Existence and behavior of positive solutions for a class of quasilinear elliptic problems with discontinuous nonlinearity ⋮ Mixed order elliptic problems driven by a singularity, a Choquard type term and a discontinuous power nonlinearity with critical variable exponents

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of solutions for a class of elliptic equations in \(\mathbb R^N\) with vanishing potentials
• Existence of solutions for an NSE with discontinuous nonlinearity
• Some discontinuous variational problems
• Nonlinear Schrödinger equations with vanishing and decaying potentials.
• Variational methods for non-differentiable functionals and their applications to partial differential equations
• Finite-amplitude steady waves in stratified fluids
• On a class of nonlinear Schrödinger equations
• Remarks on the Schrödinger operator with singular complex potentials
• The dual variational principle and elliptic problems with discontinuous nonlinearities
• Introduction à la théorie des points critiques et applications aux problèmes elliptiques
• Some discontinuous problems with a quasilinear operator
• Existence of standing waves solution for a nonlinear Schrödinger equation in \(\mathbb{R}^N\)
• Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
• Local mountain passes for semilinear elliptic problems in unbounded domains
• On existence and concentration of solutions for an elliptic problem with discontinuous nonlinearity via penalization method
• Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)_a
• Optimization and nonsmooth analysis
• Generalized Gradients and Applications
• The obstacle problem and partial differential equations with discontinuous nonlinearities
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Existence and Concentration of Solutions for a Class of Elliptic Problems with Discontinuous Nonlinearity in $\mathbf{R}^{N}$
• Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity
• An introduction to minimax theorems and their applications to differential equations

This page was built for publication: Existence and behavior of positive solution for a problem with discontinuous nonlinearity in \({\mathbb{R}}^N\) via a nonsmooth penalization