The concentration-compactness principles for \(W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)\) and application

DOI10.1515/anona-2020-0160zbMath1467.35336arXiv1909.09379OpenAlexW3112437528MaRDI QIDQ2035491

Ky Ho, Yun-Ho Kim

Publication date: 24 June 2021

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.09379

zbMATH Keywords

variational methodsfractional \(p\)-Laplacian\(p(\cdot)\)-Laplacianconcentration-compactness principlescritical imbeddingfractional Sobolev spaces with variable exponents

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33) Existence of solutions for minimax problems (49J35) Weak solutions to PDEs (35D30) Variational methods for second-order elliptic equations (35J20) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (13)

Fractional double phase Robin problem involving variable order-exponents without Ambrosetti-Rabinowitz condition ⋮ Infinitely many solutions for a doubly nonlocal fractional problem involving two critical nonlinearities ⋮ Singular elliptic problem involving a fractional \(p\)-Laplacian with discontinuous nonlinearity ⋮ On critical variable-order Kirchhoff type problems with variable singular exponent ⋮ Existence and multiplicity of solutions for critical nonlocal equations with variable exponents ⋮ Multiplicity results for double phase problems involving a new type of critical growth ⋮ Small perturbations of critical nonlocal equations with variable exponents ⋮ Local regularity for nonlocal equations with variable exponents ⋮ The concentration-compactness principle for the nonlocal anisotropic \(p\)-Laplacian of mixed order ⋮ Fractional double phase Robin problem involving variable‐order exponents and logarithm‐type nonlinearity ⋮ Weak solutions for some fractional singular \((p, q)\)-Laplacian nonlocal problems with Hardy potential ⋮ Existence of solutions for a class of fractional Kirchhoff-type systems in \(\mathbb{R}^N\) with non-standard growth ⋮ Critical Kirchhoff \(p(\cdot) \& q(\cdot)\)-fractional variable-order systems with variable exponent growth

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