Infinitely many solutions for a doubly nonlocal fractional problem involving two critical nonlinearities

DOI10.1080/17476933.2021.1951719zbMath1501.35444OpenAlexW3203323954MaRDI QIDQ5049165

Akasmika Panda, Debajyoti Choudhuri

Publication date: 11 November 2022

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2021.1951719

zbMATH Keywords

genussymmetric mountain pass lemmaconcentration compactness principlefractional \(p(x)\)-Laplace operatorfractional Sobolev space with variable exponent

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33) Weak solutions to PDEs (35D30) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

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Cites Work

• Unnamed Item
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• Nonlocal problems at nearly critical growth
• On some critical problems for the fractional Laplacian operator
• Hitchhiker's guide to the fractional Sobolev spaces
• The Brezis-Nirenberg problem for the fractional \(p\)-Laplacian
• The Pohozaev identity for the fractional Laplacian
• Mountain pass solutions for non-local elliptic operators
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• 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
• A multi-phase transition model for dislocations with interfacial microstructure
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• The principle of concentration compactness in \(L^{p(x)}\) spaces and its application
• Digital picture processing. An introduction. Transl. from the Russian
• On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent
• Comparison and sub-supersolution principles for the fractional \(p(x)\)-Laplacian
• Multiplicity results for fractional Laplace problems with critical growth
• The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem
• On a fractional \(p \& q\) Laplacian problem with critical Sobolev-Hardy exponents
• Three solutions for a nonlocal problem with critical growth
• Concentration-compactness principle at infinity and semilinear elliptic equations involving critical and subcritical Sobolev exponents
• Multiplicity results for \((p,q)\) fractional elliptic equations involving critical nonlinearities
• Superlinear Schrödinger-Kirchhoff type problems involving the fractional \(p\)-Laplacian and critical exponent
• Recent developments in problems with nonstandard growth and nonuniform ellipticity
• The concentration-compactness principles for \(W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)\) and application
• Fractional \(p \& q\) Laplacian problems in \(\mathbb{R}^N\) with critical growth
• Renormalized solutions for the fractional \(p(x)\)-Laplacian equation with \(L^1\) data
• Regularity for minimizers for functionals of double phase with variable exponents
• A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional \(p(\cdot)\)-Laplacian
• A Sobolev non embedding
• Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
• A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
• Fractional eigenvalues
• Bifurcation and multiplicity results for critical fractionalp-Laplacian problems
• Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• The concentration-compactness principle for variable exponent spaces and applications
• Nonlocal Operators with Applications to Image Processing
• Variational Methods for Nonlocal Fractional Problems
• Fractional Sobolev spaces with variable exponents and fractional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mrow> <mml:mo form="prefix">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo form="postfix">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math>-Laplacians
• Existence of sign-changing solution for a problem involving the fractional Laplacian with critical growth nonlinearities
• Partial Differential Equations with Variable Exponents
• Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves
• Deblurring and Denoising of Images by Nonlocal Functionals
• Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity