1,720,988 research outputs found
Multiple solutions for a class of Schroedinger equations involving the fractional p–Laplacian
No full textWe deal with the multiplicity of weak solutions of the non-local elliptic equation in , where is the so-called fractional -Laplacian, is a suitable continuous potential and the nonlinearity grows as at infinity. Our results extend the classical local counterpart, that is when
On certain nonlocal Hardy-Sobolev critical elliptic Dirichlet problems
No full textThis paper deals with the existence, multiplicity and the asymptotic behavior of nontrivial solutions for nonlinear Dirichlet problems in bounded domains, driven by the fractional Laplace operator and involving a critical Hardy potential and real parameters with physical meaning. The nonlinear term f is subcritical, while the nonlinear function g could be either a critical term or a perturbation
(p,q) systems with critical terms in RN
No full textThis paper deals with the existence of nontrivial solutions for critical Hardy quasilinear systems (S) driven by general (p,q) elliptic perators of Marcellini types. Existence is derived as an application of the concentration-compactness principle of Lions via the mountain pass geometry. The constructed solution has both components nontrivial, that is it solves the actual system, which does not reduce into an equation. We present also a simplified version (S') of the main system (S) , which is anyway interesting. We exhibit a new proof for the existence of nontrivial solutions of (S') , which is more direct and elegant. However, the assumptions for both systems (S) and (S') are milder and in any case much different from the usual requests granted in related problems. Finally, the results improve or complement previous theorems for the quasilinear (p,q) scalar as well as vectorial problems
Bifurcation and multiplicity results for critical nonlocal fractional Laplacian problems
Full text linkIn this paper we consider a critical nonlocal problem and we prove a multiplicity and bifurcation result for this, using a classical theorem in critical points theory. Precisely, we show that in a suitable left neighborhood of any eigenvalue of the operator which drives the equation the number of nontrivial solutions for the problem under consideration is at least twice the multiplicity of the eigenvalue. Hence, we extend a famous result got by Cerami, Fortunato and Struwe for classical elliptic equations, to the case of nonlocal fractional operators
Kirchhoff–Hardy Fractional Problems with Lack of Compactness
No full textAbstract
This paper deals with the existence and the asymptotic behavior of nontrivial solutions for some classes of stationary Kirchhoff problems driven by a fractional integro-differential operator and involving a Hardy potential and different critical nonlinearities. In particular, we cover the delicate degenerate case, that is, when the Kirchhoff function M is zero at zero. To overcome the difficulties due to the lack of compactness as well as the degeneracy of the models, we have to make use of different approaches.</jats:p
Degenerate Kirchhoff (p, q)–Fractional Systems with Critical Nonlinearities
No full textThis paper deals with the existence of nontrivial solutions for critical possibly degenerate Kirchhoff fractional (p,q) systems. For clarity, the results are first presented in the scalar case, and then extended into the vectorial framework.
The main features and novelty of the paper are the (p,q) growth of the fractional operator, the double lack of compactness as well as the fact that the systems can be degenerate. As far as we know the results are new even in the scalar case and when the Kirchhoff model considered is non-degenerate
P-fractional hardy-schrodinger-kirchhoff systems with critical nonlinearities
No full textThis paper deals with the existence of nontrivial solutions for critical Hardy-Schrodinger-Kirchhoff systems driven by the fractional p-Laplacian operator. Existence is derived as an application of the mountain pass theorem and the Ekeland variational principle. The main features and novelty of the paper are the presence of the Hardy terms as well as critical nonlinearities8111111131CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP37877491859909822017/19752-
Existence of entire solutions for Schrödinger–Hardy systems involving two fractional operators
No full textThis paper deals with the existence of nontrivial nonnegative solutions of Schrödinger-Hardy systems driven by two possibly different
fractional p-Laplacian operators, via various variational methods. The main features of the paper are the presence of the Hardy terms
and the fact that the nonlinearities do not necessarily satisfy the Ambrosetti--Rabinowitz condition. Moreover, we consider systems including critical nonlinear terms, as treated very recently in literature, and present radial versions of the main theorems. Finally, we briefly show how to extend the previous results when the fractional Laplacian operators are replaced by more general elliptic nonlocal integro-differential operators
Multiplicity results for magnetic fractional problems
No full textThe paper deals with the existence of multiple solutions for a boundary value problem driven by the magnetic fractional Laplacian. We prove that the problem admits at least two nontrivial weak solutions under two different sets of conditions on the nonlinear term f which are dual in a suitable sense
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