Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity

DOI10.1063/1.5107517zbMath1427.35063arXiv1808.02469OpenAlexW2885560739MaRDI QIDQ5205155

Sekhar Ghosh, Kamel Saoudi, Debajyoti Choudhuri

Publication date: 10 December 2019

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.02469

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Variational methods applied to PDEs (35A15) Nonlinear elliptic equations (35J60) Analyticity in context of PDEs (35A20) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30)

Related Items (23)

Elliptic problem driven by different types of nonlinearities ⋮ Existence of solution for a system involving a singular-nonlocal operator, a singularity and a Radon measure ⋮ Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity ⋮ An existence result for singular nonlocal fractional Kirchhoff–Schrödinger–Poisson system ⋮ Dirichlet problems for fractional Laplace equations with singular nonlinearity ⋮ Singular non local problem with gradient term ⋮ On elliptic problems with Choquard term and singular nonlinearity ⋮ Multiplicity of Solutions to a p-q Fractional Laplacian System with Concave Singular Nonlinearities ⋮ Existence of multiple solution for a singular \(p(x)\)-Laplacian problem ⋮ Unnamed Item ⋮ A multiplicity results to a p-q Laplacian system with a concave and singular nonlinearities ⋮ Eigenvalue for a problem involving the fractional \((p, q)\)-Laplacian operator and nonlinearity with a singular and a supercritical Sobolev growth ⋮ Algebraic topological techniques for elliptic problems involving fractional Laplacian ⋮ Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method ⋮ Existence of positive solutions for a singular elliptic problem with critical exponent and measure data ⋮ Existence and multiplicity of solutions for a nonlocal problem with critical Sobolev-Hardy nonlinearities ⋮ Existence and Hölder regularity of infinitely many solutions to a \(p\)-Kirchhoff-type problem involving a singular nonlinearity without the Ambrosetti-Rabinowitz (AR) condition ⋮ A critical fractional Choquard problem involving a singular nonlinearity and a Radon measure ⋮ Existence of multiple solutions to Schrödinger-Poisson system in a nonlocal set up in \(\mathbb{R}^3\) ⋮ Nonlocal fractional system involving the fractional \(p, q\)-Laplacians and singular potentials ⋮ A singular elliptic problem involving fractional p-Laplacian and a discontinuous critical nonlinearity ⋮ Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity ⋮ Infinitely many large solutions to a variable order nonlocal singular equation

Cites Work

• Unnamed Item
• Unnamed Item
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• Nonlocal problems at nearly critical growth
• The second eigenvalue of the fractional \(p\)-Laplacian
• Local behavior of fractional \(p\)-minimizers
• Existence of multiple solutions to a partial differential equation involving the fractional \(p\)-Laplacian
• Global bifurcation and local multiplicity results for elliptic equations with singular nonlinearity of super exponential growth in \(\mathbb R^2\)
• Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian
• A critical fractional equation with concave-convex power nonlinearities
• The Brezis-Nirenberg problem for the fractional \(p\)-Laplacian
• Global Hölder regularity for the fractional \(p\)-Laplacian
• Nonlocal problems with singular nonlinearity
• Mountain pass solutions for non-local elliptic operators
• Neighborhood filters and PDE's
• A general mountain pass principle for locating and classifying critical points
• Multiplicity of positive solutions for a singular and critical problem
• Multiplicity results for a singular and quasilinear equation
• \(W^{1,p}_0\) versus \(C^1\) local minimizers for a singular and critical functional
• Digital picture processing. An introduction. Transl. from the Russian
• Regularity and stability for the mathematical programming problem in Banach spaces
• Combined effects of concave and convex nonlinearities in some elliptic problems
• Entropy solution for a nonlinear elliptic problem with lower order term in Musielak-Orlicz spaces
• A critical fractional elliptic equation with singular nonlinearities
• Multiplicity and asymptotic behavior of positive solutions for a singular semilinear elliptic problem.
• Variational methods for non-local operators of elliptic type
• A Brezis-Nirenberg result for non-local critical equations in low dimension
• Fractional Brownian motion via fractional Laplacian
• Dual variational methods in critical point theory and applications
• A Brezis-Nirenberg splitting approach for nonlocal fractional equations
• \(H^s\) versus \(C^0\)-weighted minimizers
• Lower semicontinuity of functionals of fractional type and applications to nonlocal equations with critical Sobolev exponent
• Semilinear elliptic equations with singular nonlinearities
• On Dirichlet problem for fractional \(p\)-Laplacian with singular non-linearity
• Existence of multiple positive solutions for singular elliptic problems with concave and convex nonlinearities
• Fractional eigenvalues
• Critical growth fractional elliptic problem with singular nonlinearities
• A concave—convex elliptic problem involving the fractional Laplacian
• From the long jump random walk to the fractional Laplacian
• On a singular nonlinear dirichlet problem
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• On a Singular Nonlinear Elliptic Boundary-Value Problem
• MULTIPLICITY OF POSITIVE SOLUTIONS FOR A SINGULAR AND CRITICAL ELLIPTIC PROBLEM IN ℝ²
• An elliptic equation with singular nonlinearity
• On a dirichlet problem with a singular nonlinearity
• On the Fredholm alternative for the p-Laplacian at the first eigenvalue
• The Nehari manifold for a singular elliptic equation involving the fractional Laplace operator
• Fractional p-eigenvalues
• On vs. local minimizers for a critical functional related to fractionalp-Laplacian
• Deblurring and Denoising of Images by Nonlocal Functionals
• Minimum Value for c in the Sobolev Inequality $\| {\phi ^3 } \|\leqq c\| {\nabla \phi } \|^3 $
• A multiplicity results for a singular problem involving the fractionalp-Laplacian operator
• Combined effects of singular and superlinear nonlinearities in some singular boundary value problems.
• The uniform Hopf inequality for discontinuous coefficients and optimal regularity in BMO for singular problems

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