Existence of positive solutions for a class of \(p\&q\) elliptic problems with critical growth on \(\mathbb R^N\)
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Publication:633652
DOI10.1016/j.jmaa.2011.02.017zbMath1211.35114OpenAlexW1967016508MaRDI QIDQ633652
Publication date: 29 March 2011
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.02.017
Nonlinear elliptic equations (35J60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Variational methods for second-order elliptic equations (35J20) Positive solutions to PDEs (35B09)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence of radial solutions for a class of \(p(x)\)-Laplacian equations with critical growth.
- Existence of solutions for quasilinear elliptic equations
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- The concentration-compactness principle in the calculus of variations. The limit case. I
- Multiple solutions for the p\&q-Laplacian problem with critical exponents
- Multiplicity of solutions for a quasilinear elliptic problem via the cohomological index
- The existence of nontrivial solutions to nonlinear elliptic equation of \(p\)-\(q\)-Laplacian type on \(\mathbb R^N\)
- A class of \(p\)-\(q\)-Laplacian type equation with potentials eigenvalue problem in \(\mathbb{R}^N\)
- The existence of a nontrivial solution to the \(p{\&}q\)-Laplacian problem with nonlinearity asymptotic to \(u^{p - 1}\) at infinity in \(\mathbb R^N\)
- A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
- Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
- Some properties of weak solutions of nonlinear scalar field equations
- Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term
- On harnack type inequalities and their application to quasilinear elliptic equations
- On perturbations of a class of a periodic \(m\)-Laplacian equation with critical growth
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