The Brézis-Nirenberg equation for the \((m,p)\) Laplacian in the whole space

DOI10.3934/dcdss.2023068OpenAlexW4362644049MaRDI QIDQ6149435

Patrizia Pucci, Lin-Lin Wang

Publication date: 5 February 2024

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2023068

zbMATH Keywords

critical exponentexistence of entire solutions\((m,p)\)-Laplacian

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Cites Work

• Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations
• Existence of entire solutions for a class of quasilinear elliptic equations
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• On a class of critical \((p,q)\)-Laplacian problems
• Local and global properties of solutions of quasilinear elliptic equations
• Best constant in Sobolev inequality
• The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem
• Recent developments in problems with nonstandard growth and nonuniform ellipticity
• Classification of positive \(\mathcal{D}^{1, p}(\mathbb{R}^N)\)-solutions to the critical \(p\)-Laplace equation in \(\mathbb{R}^N\)
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Extrema problems with critical sobolev exponents on unbounded domains
• Entire solutions for some critical equations in the Heisenberg group
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