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Nonlocal problems with singular nonlinearity
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In this article, the existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities were investigated.Abstract:
We investigate existence and uniqueness of solutions for a class of nonlinear nonlocal problems involving the fractional $p$-Laplacian operator and singular nonlinearities.read more
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Recent Progresses in the Theory of Nonlinear Nonlocal Problems
Sunra Mosconi,Marco Squassina +1 more
TL;DR: In this paper, the authors overview some recent existence and regularity results in the theory of nonlocal nonlinear problems driven by the fractional p-Laplacian, and give an overview of some of the results.
Journal ArticleDOI
Combined effects of Choquard and singular nonlinearities in fractional Kirchhoff problems
Fuliang Wang,Die Hu,Mingqi Xiang +2 more
TL;DR: In this paper, the existence and multiplicity of solutions for a class of fractional Kirchho problems involving Choquard type nonlinearity and singular non-linearity were studied.
Journal ArticleDOI
Multiplicity and H\"{o}lder regularity of solutions for a nonlocal elliptic PDE involving singularity
TL;DR: In this article, the existence of multiple solutions for a nonlinear nonlocal elliptic PDE involving a singularity was proved for some ε = 0, β = 0.
Journal ArticleDOI
Fractional Sobolev inequalities associated with singular problems
Grey Ercole,Gilberto A. Pereira +1 more
TL;DR: In this article, Sobolev type inequalities associated with singular problems for the fractional p-Laplacian operator in a bounded domain of RN, N ≥ 2, were studied.
References
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Journal ArticleDOI
On a dirichlet problem with a singular nonlinearity
TL;DR: In this article, a dirichlet problem with singular nonlinearity is considered, and the authors present a communication in Partial Differential Equations (PDE) approach to solve it.
Journal ArticleDOI
On a singular nonlinear elliptic boundary-value problem
Alan C. Lazer,P. J. McKenna +1 more
TL;DR: In this paper, the authors considered the singular boundary value problem with the assumption that p(x) > 0 and certain smoothness assumptions, and showed that there exists a solution which is smooth on Q2 and continuous on Q.
Journal ArticleDOI
Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
TL;DR: In this article, weak and strong comparison theorems for solutions of differential inequalities involving a class of elliptic operators that includes the p-laplacian operator were proved. And these theorem together with the method of moving planes and the sliding method were used to get symmetry and monotonicity properties of solutions to quasilinear elliptic equations in bounded domains.
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Semilinear elliptic equations with singular nonlinearities
Lucio Boccardo,Luigi Orsina +1 more
TL;DR: In this paper, the authors prove existence, regularity and nonexistence results for problems whose model is γ > 0 and f is a nonnegative function on the boundary of an open, bounded subset of the Euclidean space.
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