Existence and multiplicity of solutions for critical nonlocal equations with variable exponents
DOI10.1080/00036811.2022.2107916zbMath1523.35285OpenAlexW4289593684MaRDI QIDQ6055920
Patrizia Pucci, Sihua Liang, Binlin Zhang
Publication date: 29 September 2023
Published in: Applicable Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00036811.2022.2107916
variational methodsfractional \(p\)-Laplacian\(p(\cdot)\)-Laplacianconcentration-compactness principles
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)
Related Items (2)
Cites Work
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- Critical stationary Kirchhoff equations in \(\mathbb R^N\) involving nonlocal operators
- Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations
- Existence and multiplicity of solutions for a \(p(x)\)-Laplacian equation with critical growth
- Hitchhiker's guide to the fractional Sobolev spaces
- Existence of solutions for Kirchhoff type problem involving the non-local fractional \(p\)-Laplacian
- Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity
- Lebesgue and Sobolev spaces with variable exponents
- The concentration-compactness principle in the calculus of variations. The locally compact case. I
- Multiple solutions for nonhomogeneous Schrödinger-Kirchhoff type equations involving the fractional \(p\)-Laplacian in \(\mathbb R^N\)
- The concentration-compactness principle in the calculus of variations. The locally compact case. II
- Existence of solutions for \(p(x)\)-Laplacian problem on an unbounded domain
- Compact imbeddings between variable exponent spaces with unbounded underlying domain
- Global solvability for the degenerate Kirchhoff equation with real analytic data
- On some variational problems
- Multiplicity results for variable-order fractional Laplacian equations with variable growth
- 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
- The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem
- Concentration-compactness principle at infinity and semilinear elliptic equations involving critical and subcritical Sobolev exponents
- Minimax theorems
- Infinitely many small solutions for the \( p (x)\)-Laplacian operator with nonlinear boundary conditions
- Multiplicity results for \((p,q)\) fractional elliptic equations involving critical nonlinearities
- The concentration-compactness principles for \(W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)\) and application
- Degenerate Kirchhoff \((p, q)\)-fractional systems with critical nonlinearities
- Dual variational methods in critical point theory and applications
- A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional \(p(\cdot)\)-Laplacian
- Existence results for Schrödinger \(p(\cdot)\)-Laplace equations involving critical growth in \(\mathbb{R}^N$
- Multiple solutions for noncooperative \(p(x)\)-Laplacian equations in \(\mathbb R^N\) involving the critical exponent
- Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain
- Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
- Existence and multiplicity of entire solutions for fractional \(p\)-Kirchhoff equations
- A critical Kirchhoff type problem involving a nonlocal operator
- Infinitely many solutions for the stationary Kirchhoff problems involving the fractionalp-Laplacian
- Non-local Diffusions, Drifts and Games
- Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
- The concentration-compactness principle for variable exponent spaces and applications
- Variational Methods for Nonlocal Fractional Problems
- Multiple solutions for a class of p ( x )-Laplacian equations in involving the critical exponent
- A multiplicity result for quasilinear elliptic equations involving critical sobolev exponents
- 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
- On symmetric solutions of an elliptic equation with a nonlinearity involving critical Sobolev exponent
- Extrema problems with critical sobolev exponents on unbounded domains
- Existence and multiplicity of solutions for fractional p(x,.)-Kirchhoff-type problems in ℝN
- Homoclinic solutions for Hamiltonian systems with variable-order fractional derivatives
- Infinitely many solutions for Kirchhoff-type variable-order fractional Laplacian problems involving variable exponents
- Sobolev embeddings for unbounded domain with variable exponent having values across N
- A Brezis-Nirenberg type result for a nonlocal fractional operator
- An Extension Problem Related to the Fractional Laplacian
- Variable Exponent, Linear Growth Functionals in Image Restoration
- Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
- On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
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