Infinitely many solutions for a class of fourth order elliptic equations in \(\mathbb R^N\)

DOI10.1007/s10114-008-5423-1zbMath1154.35335OpenAlexW1970822785MaRDI QIDQ2519335

Zifei Shen, Min-Bo Yang

Publication date: 26 January 2009

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-008-5423-1

zbMATH Keywords

Palais-Smale conditionbiharmonic operatorHardy-Sobolev critical exponent

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Nonlinear elliptic equations (35J60) Variational methods for higher-order elliptic equations (35J35)

Related Items (7)

Infinitely many solutions for a class of biharmonic equations with indefinite potentials ⋮ Infinitely many solutions for fourth-order elliptic equations ⋮ Unnamed Item ⋮ Existence of positive ground solutions for biharmonic equations via Pohožaev-Nehari manifold ⋮ Infinitely many solutions for fourth-order elliptic equations with general potentials ⋮ Infinitely many solutions for fourth-order semilinear \(\Delta_{\gamma}\)-Laplace equation in \(\mathbb{R}^N\) ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The limit case. II
• On multiple solutions of quasilinear equations involving the critical Sobolev exponent
• Existence and nonexistence results for critical growth biharmonic elliptic equations
• On some fourth-order semilinear elliptic problems in \(\mathbb R^N\)
• A fourth order elliptic equation with nonlinear boundary conditions
• Positive solutions in semilinear critical problems for polyharmonic operators
• A concentration-compactness lemma with applications to singular eigenvalue problems
• On multiple solutions of a singular quasilinear equation on unbounded domain.
• On a class of singular biharmonic problems involving critical exponents.
• Dual variational methods in critical point theory and applications
• Critical exponents and critical dimensions of polyharmonic operators
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Critical semilinear biharmonic equations in R^N
• An integral representation theorem for lower semicontinuous envelopes of integral functionals
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
• Nontrivial solutions for a class of semilinear biharmonic problems involving critical exponents

This page was built for publication: Infinitely many solutions for a class of fourth order elliptic equations in \(\mathbb R^N\)