Existence and multiplicity of positive solutions to a \(p\)-Laplacian equation in \(\mathbb R^N\).
From MaRDI portal
Publication:601541
zbMath1212.35107MaRDI QIDQ601541
Giovany M. Figueiredo, Claudianor Oliveira Alves
Publication date: 28 October 2010
Published in: Differential and Integral Equations (Search for Journal in Brave)
existencemultiplicityPalais-Smale conditionpositive solutionAmbrosetti-Rabinowitz superlinear condition
Variational methods involving nonlinear operators (47J30) Singular perturbations in context of PDEs (35B25) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Positive solutions to PDEs (35B09)
Related Items
Existence and concentration of positive solutions for a class of discontinuous quasilinear Schrödinger problems in \(\mathbb{R}^N \) ⋮ A multiplicity result via Ljusternick-Schnirelmann category and Morse theory for a fractional Schrödinger equation in \(\mathbb{R}^N\) ⋮ Fitzhugh-Nagumo system with zero mass and critical growth ⋮ On existence of multiple normalized solutions to a class of elliptic problems in whole \(\mathbb{R}^N\) ⋮ Existence of a positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in \({\mathbb{R}^{2}}\) ⋮ On multiplicity and concentration of positive solutions for a class of quasilinear problems with critical exponential growth in \(\mathbb R^{N}\) ⋮ A multiplicity result for a nonlinear fractional Schrödinger equation in \(\mathbb{R}^N\) without the Ambrosetti-Rabinowitz condition ⋮ Semiclassical states of p-Laplacian equations with a general nonlinearity in critical case ⋮ On a class of nonlocal Schrödinger equations with exponential growth ⋮ Multiple solutions for singularly perturbed nonlinear magnetic Schrödinger equations ⋮ Existence and multiplicity results for some Schrödinger-Poisson system with critical growth ⋮ Ground states for a class of quasilinear elliptic systems with critical exponent ⋮ Existence and concentration behavior of solutions for a class of quasilinear elliptic equations with critical growth ⋮ On Existence of Multiple Normalized Solutions to a Class of Elliptic Problems in Whole \(\mathbb{R}^N\) via Lusternik-Schnirelmann Category ⋮ The nonlinear \((p,q)\)-Schrödinger equation with a general nonlinearity: existence and concentration ⋮ Existence of multiple solutions for a Schrödinger logarithmic equation via Lusternik–Schnirelmann category ⋮ On the uniform vanishing property at infinity of \(W^{s, p}\)-sequences ⋮ Existence and concentration of solutions for a class of biharmonic equations ⋮ Multiple solutions for a Schrödinger–Bopp–Podolsky system with positive potentials ⋮ Nonhomogeneous equations with critical exponential growth and lack of compactness ⋮ Existence of a positive solution for a class of elliptic problems in exterior domains involving critical growth ⋮ Multiplicity and concentration of positive solutions for the Schrödinger-Poisson equations ⋮ Nonlinear perturbations of a periodic Kirchhoff equation in \(\mathbb R^N\) ⋮ Existence, regularity, and concentration phenomenon of nontrivial solitary waves for a class of generalized variable coefficient Kadomtsev-Petviashvili equation ⋮ Variational Methods for Schrödinger Type Equations ⋮ Nonlinear perturbations of a periodic Kirchhoff-Boussinesq-type problems in \(\mathbb{R}^N\) ⋮ On bounded variation solutions of quasi-linear 1-Laplacian problems with periodic potential in \(\mathbb{R}^N\) ⋮ POSITIVE GROUND STATES FOR A CLASS OF SUPERLINEAR -LAPLACIAN COUPLED SYSTEMS INVOLVING SCHRÖDINGER EQUATIONS ⋮ Existence of weak solutions for a quasilinear equation in \(\mathbb R^N\) ⋮ Existence, multiplicity, and concentration of positive solutions for a quasilinear Choquard equation with critical exponent ⋮ Normalized solutions for p-Laplacian equations with a \(L^2\)-supercritical growth ⋮ On existence and concentration of solutions for an elliptic problem with discontinuous nonlinearity via penalization method ⋮ On the multiplicity and concentration of positive solutions for a class of quasilinear problems in \(\mathbb{R}^N\) ⋮ Existence and concentration of positive solutions for a Schrödinger logarithmic equation ⋮ Existence of semiclassical states for a quasilinear Schrödinger equation on \(\mathbb{R}^{N}\) with exponential critical growth ⋮ On fractional Schr$\ddot{\mbox{o}}$ödinger equation in $\mathbb {R}^{N}$RN with critical growth ⋮ Existence and multiplicity of solutions for a class of quasilinear problems in Orlicz-Sobolev spaces without Ambrosetti-Rabinowitz condition ⋮ Existence of infinitely many solutions for \(p\)-Laplacian equations in \(\mathbb{R}^N\) ⋮ Multiplicity and concentration of solutions for a quasilinear Choquard equation ⋮ Solutions of semiclassical states for perturbed \( p\)-Laplacian equation with critical exponent ⋮ The existence of semiclassical states for some \(p\)-Laplacian equation with critical exponent ⋮ Multiplicity of positive solutions for a class of elliptic equations in divergence form ⋮ Semiclassical solutions of perturbed \(p\)-Laplacian equations with critical nonlinearity ⋮ On the multiplicity and concentration for \(p\)-fractional Schrödinger equations ⋮ Multiplicity results for the fractional Laplacian in expanding domains ⋮ \((p,N)\) equations with critical exponential nonlinearities in \(\mathbb{R}^N\) ⋮ Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional \(p\)-Laplacian ⋮ On the energy functionals derived from a non-homogeneous \(p\)-Laplacian equation: \(\Gamma\)-convergence, local minimizers and stable transition layers ⋮ Existence of semiclassical ground state solutions for a generalized Choquard equation ⋮ Multiplicity and concentration of positive solutions for a class of quasilinear problems through Orlicz-Sobolev space ⋮ On ground states of superlinear \(p\)-Laplacian equations in R\(^N\) ⋮ Existence and concentration behavior of positive solutions for a quasilinear Schrödinger equation ⋮ On a class of Kirchhoff problems via local mountain pass
