Existence and multiplicity of solutions for a Schrödinger-Kirchhoff type equation involving the fractional \(p(.,.)\)-Laplacian operator in \(\mathbb{R}^N\)

DOI10.1007/s13348-020-00283-5zbMath1458.35444OpenAlexW3008457598MaRDI QIDQ2228329

Gülizar Alisoy, Yeşim Saraç, Rabil Ayazoglu (Mashiyev), Sıdıka Şule Şener

Publication date: 17 February 2021

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13348-020-00283-5

zbMATH Keywords

mountain pass theoremKrasnoselskii's genusfractional Sobolev space with variable exponentfractional \(p(., .)\)-Laplacian operator

Mathematics Subject Classification ID

Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11)

Related Items (9)

Existence and multiplicity of solutions for Schrödinger-Kirchhoff type problems involving the fractional \(p(\cdot) \)-Laplacian in \(\mathbb{R}^N\) ⋮ On a new fractional Sobolev space with variable exponent on complete manifolds ⋮ Local regularity for nonlocal equations with variable exponents ⋮ Morse's theory and local linking for a fractional \((p_1 (\mathrm{x}.,), p_2 (\mathrm{x}.,))\): Laplacian problems on compact manifolds ⋮ Fractional Sobolev spaces with kernel function on compact Riemannian manifolds ⋮ Existence and Multiplicity of Solutions for a Class of Fractional Kirchhoff Type Problems with Variable Exponents ⋮ On a class of fractional p (⋅,⋅)−Laplacian problems with sub-supercritical nonlinearities ⋮ Infinitely many solutions to a Kirchhoff-type equation involving logarithmic nonlinearity via Morse's theory ⋮ A concave–convex Kirchhoff type elliptic equation involving the fractionalp-Laplacian and steep well potential

Cites Work

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• Existence results for fractional \(p\)-Laplacian problems via Morse theory
• Critical stationary Kirchhoff equations in \(\mathbb R^N\) involving nonlocal operators
• Existence of multiple solutions of Kirchhoff type equation with sign-changing potential
• Existence of one weak solution for \(p(x)\)-biharmonic equations with Navier boundary conditions
• Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations
• Hitchhiker's guide to the fractional Sobolev spaces
• Multiple solutions for a class of fractional Schrödinger equations in \(\mathbb{R}^N\)
• Uniform estimates and limiting arguments for nonlocal minimal surfaces
• Lebesgue and Sobolev spaces with variable exponents
• Sequences of weak solutions for fractional equations
• Mountain pass solutions for non-local elliptic operators
• Stability of variational eigenvalues for the fractional \(p\)-Laplacian
• Ground state solutions of scalar field fractional Schrödinger equations
• A symmetry result for a general class of divergence form PDEs in fibered media
• On superlinear \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• On a \(p\)-Kirchhoff equation via Krasnoselskii's genus
• Fractional quantum mechanics and Lévy path integrals
• 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
• Eigenvalue problems involving the fractional \(p(x)\)-Laplacian operator
• Existence and multiplicity of solutions for Kirchhoff-Schrödinger type equations involving \(p(x)\)-Laplacian on the entire space \(\mathbb{R}^N\)
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• On a Schrödinger-Kirchhoff-type equation involving the \(p(x)\)-Laplacian
• On a class of fractional Laplacian problems with variable exponents and indefinite weights
• Existence of multiple solutions for nonhomogeneous Schrödinger-Kirchhoff system involving the fractional \(p\)-Laplacian with sign-changing potential
• Infinitely many solutions for the stationary fractional \(p\)-Kirchhoff problems in \(\mathbb{R}^N\)
• On a nonlocal fractional \(p\)(., .)-Laplacian problem with competing nonlinearities
• Eigenvalue problems for fractional \(p(x,y)\)-Laplacian equations with indefinite weight
• A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional \(p(\cdot)\)-Laplacian
• A new result on high energy solutions for Schrödinger-Kirchhoff type equations in \(\mathbb R^N\)
• Elliptic problems involving the fractional Laplacian in \(\mathbb R^N\)
• A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations
• A critical Kirchhoff type problem involving a nonlocal operator
• Electrorheological Fluids Equations Involving Variable Exponent with Dependence on the Gradient via Mountain Pass Techniques
• Multiplicity of solutions for a class of quasilinear Kirchhoff system involving the fractionalp-Laplacian
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Existence and symmetry results for a Schr\"odinger type problem involving the fractional Laplacian
• Non-local Diffusions, Drifts and Games
• Stationary waves of Schrödinger-type equations with variable exponent
• 𝑝(𝑥)-Laplacian with indefinite weight
• NONLINEAR SCHRÖDINGER EQUATIONS WITH STEEP POTENTIAL WELL
• Multiple small solutions for<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>-Schrödinger equations with local sublinear nonlinearities via genus theory
• 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 existence solution for Schrödinger–Kirchhoff-type equations involving the fractional p-Laplacian in ℝ^N
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• Partial Differential Equations with Variable Exponents
• Infinitely many solutions for a class of stationary Schrödinger equations with non-standard growth
• Ground state solutions for nonlinear fractional Schrödinger equations in $\mathbb {R}^N$RN
• Multiple solutions for Kirchhoff-type equations in $\mathbb {R}^N$RN

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