Singular elliptic problems in \(\mathbb R^N\) with critical Sobolev-Hardy exponents

DOI10.1016/j.na.2006.12.027zbMath1156.35029OpenAlexW2191963793MaRDI QIDQ2474359

Dongsheng Kang, Shuangjie Peng

Publication date: 6 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.2006.12.027

zbMATH Keywords

variational methodssingularitynontrivial solutioncritical Sobolev-Hardy exponents

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)

Related Items

Fractional Hardy-Sobolev elliptic problems ⋮ Hardy-Sobolev equation on compact Riemannian manifolds involving \(p\)-Laplacian

Cites Work

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• A nonlinear elliptic PDE with the inverse square potential.
• A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics
• 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.
• Caffarelli--Kohn--Nirenberg inequalities with remainder terms.
• 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
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• Singular minimization problems
• Dual variational methods in critical point theory and applications
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• On the Best Constant for a Weighted Sobolev-Hardy Inequality
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
• Selected new aspects of the calculus of variations in the large
• A global compactness result for singular elliptic problems involving critical Sobolev exponent
• Existence of solutions for singular critical growth semilinear elliptic equations