On the quasilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy terms

DOI10.1016/j.na.2007.01.024zbMath1135.35042OpenAlexW2062075681MaRDI QIDQ2475151

Dongsheng Kang

Publication date: 10 March 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.01.024

zbMATH Keywords

quasilinear elliptic equationpositive solutionvariational methodHardy inequalitySobolev-Hardy inequality

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational methods for higher-order elliptic equations (35J35)

Related Items

Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy-Sobolev exponent and singular nonlinearity ⋮ Two positive solutions for quasilinear elliptic equations with singularity and critical exponents ⋮ Quasilinear elliptic equations with Hardy terms and Hardy-Sobolev critical exponents: nontrivial solutions ⋮ An exact estimate result for a semilinear equation with critical exponent and prescribed singularity ⋮ Quasilinear elliptic problems involving multiple critical Hardy-Sobolev exponents ⋮ Multiple positive solutions for a class of quasi-linear elliptic equations involving concave-convex nonlinearities and Hardy terms ⋮ Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent ⋮ Multiple positive solutions for \(p\)-Laplace elliptic equations involving concave-convex nonlinearities and a Hardy-type term ⋮ Existence of positive solutions for a quasilinear elliptic system involving critical Sobolev-Hardy exponents and concave-convex nonlinearities ⋮ A variational approach to a singular elliptic system involving critical Sobolev-Hardy exponents and concave-convex nonlinearities ⋮ Systems of elliptic equations involving multiple critical nonlinearities and different Hardy-type terms in \(\mathbb R^N\) ⋮ Asymptotic behaviors of solutions to quasilinear elliptic equation with Hardy potential and critical Sobolev exponent ⋮ Multiplicity of positive solutions for a semilinear elliptic system with strongly coupled critical terms and concave nonlinearities ⋮ Multiplicity of positive solutions for weighted quasilinear elliptic equations involving critical Hardy-Sobolev exponents and concave-convex nonlinearities ⋮ Quasilinear elliptic problems with combined critical Sobolev-Hardy terms ⋮ Existence of multiple solutions for a nonhomogeneous p-Laplacian elliptic equation with critical Sobolev-Hardy exponent ⋮ Existence and non-existence results for quasilinear Kirchhoff problems with the Hardy-Sobolev exponent ⋮ Existence of solutions to elliptic problems with fractional p-Laplacian and multiple critical nonlinearities in the entire space \(\mathbb{R}^N\) ⋮ Existence and multiplicity of solutions to a singular elliptic system with critical Sobolev-Hardy exponents and concave-convex nonlinearities ⋮ Multiplicity of solutions for an elliptic problem with critical Sobolev-Hardy exponents and concave-convex nonlinearities ⋮ Multiplicity of positive solutions for a nonlinear equation with a Hardy potential on the Heisenberg group ⋮ Multiple symmetric results for quasilinear elliptic systems involving singular potentials and critical Sobolev exponents in \(\mathbb{R}^N\) ⋮ The existence of solutions for quasilinear elliptic problems with combined critical Sobolev-Hardy terms ⋮ Positive symmetric solutions for a class of critical quasilinear elliptic problems in \(\mathbb R^N\) ⋮ On quasi-linear equation problems involving critical and singular nonlinearities ⋮ Existence and non-existence results for fractional Kirchhoff Laplacian problems ⋮ Quasilinear elliptic systems involving critical Hardy-Sobolev and Sobolev exponents ⋮ On the singular critical quasilinear problems in \(\mathbb R^N\) ⋮ Nontrivial solutions to semilinear elliptic problems involving two critical Hardy-Sobolev exponents ⋮ Multiple positive solutions for a quasilinear elliptic problem involving critical Sobolev-Hardy exponents and concave-convex nonlinearities ⋮ Asymptotic behavior and existence results for the biharmonic problems involving Rellich potentials ⋮ Multiplicity of solutions for a class of quasilinear elliptic equation involving the critical Sobolev and Hardy exponents ⋮ Positive solutions for elliptic problems involving Hardy-Sobolev-Maz'ya terms ⋮ On \(G\)-symmetric solutions of a quasilinear elliptic equation involving critical Hardy-Sobolev exponent ⋮ Nonlocal elliptic systems involving critical Sobolev-Hardy exponents and concave-convex nonlinearities ⋮ Existence and multiplicity of positive solutions for \(p\)-Laplacian elliptic equations ⋮ Elliptic systems involving the critical exponents and potentials ⋮ Multiple positive solutions for a quasilinear elliptic equation involving singular potential and critical Sobolev exponent ⋮ On the weighted elliptic problems involving multi-singular potentials and multi-critical exponents ⋮ A variational method for solving quasilinear elliptic systems involving symmetric multi-polar potentials ⋮ On singular elliptic equation with singular nonlinearities, Hardy-Sobolev critical exponent and weights ⋮ Existence of multiple solutions for quasilinear elliptic equation with critical Sobolev–Hardy terms ⋮ Multiplicity of solutions for quasilinear elliptic systems with singularity ⋮ Multiplicity results for biharmonic equations involving multiple Rellich-type potentials and critical exponents ⋮ Multiple positive solutions for quasilinear elliptic problems with combined critical Sobolev-Hardy terms ⋮ Systems of quasilinear elliptic equations involving multiple homogeneous nonlinearities

Cites Work

• Unnamed Item
• Unnamed Item
• Solutions for semilinear elliptic equations with critical exponents and Hardy potential
• Positive solutions for some singular critical growth nonlinear elliptic equations
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Hardy inequalities and some critical elliptic and parabolic problems
• The role played by space dimension in elliptic critical problems
• A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms.
• Existence of solutions for a nonlinear PDE with an inverse square potential.
• Existence of solutions for elliptic equations with critical Sobolev--Hardy exponents.
• Positive solutions for singular critical elliptic problems.
• Existence of solutions for elliptic problems with critical Sobolev-Hardy exponents
• Quasilinear elliptic problems with critical exponents and Hardy terms
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• Dual variational methods in critical point theory and applications
• Multiple positive and sign-changing solutions for a singular Schrödinger equation with critical growth
• Solutions to critical elliptic equations with multi-singular inverse square potentials
• Existence and multiplicity for perturbations of an equation involving a Hardy inequality and the critical Sobolev exponent in the whole of \(\mathbb R^N\)
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
• Selected new aspects of the calculus of variations in the large
• Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities
• Existence of solutions for singular critical growth semilinear elliptic equations

This page was built for publication: On the quasilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy terms