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Singular doubly nonlocal elliptic problems with Choquard type critical growth nonlinearities
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In this paper, a very singular and doubly nonlocal singular problem (P_\lambda) was studied and a weak comparison principle and optimal Sobolev regularity was established using critical point theory of non-smooth analysis and geometry of the energy functional.Abstract:
The theory of elliptic equations involving singular nonlinearities is well studied topic but the interaction of singular type nonlinearity with nonlocal nonlinearity in elliptic problems has not been investigated so far. In this article, we study the very singular and doubly nonlocal singular problem $(P_\lambda)$(See below). Firstly, we establish a very weak comparison principle and the optimal Sobolev regularity. Next using the critical point theory of non-smooth analysis and the geometry of the energy functional, we establish the global multiplicity of positive weak solutions.read more
Citations
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Regularity results on a class of doubly nonlocal problems
TL;DR: In this article, an issue of regularity of weak solution to the problem (see below) is addressed and the question of H s versus C 0 -weighted minimizers of the functional associated to problem (P) is investigated.
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Fractional Kirchhoff-Choquard system with upper critical exponent and singular nonlinearity
Yanbin Sang,Tsing-San Hsu +1 more
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Singular Fractional Choquard Equation with a Critical Nonlinearity and a Radon measure
TL;DR: In this paper, the existence of a positive sola for the singular critical Choquard problem with fractional power of Laplacian and a critical Hardy potential was shown to exist.
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Infinitely many solutions for The Brézis-Nirenberg problem with nonlinear Choquard equations
TL;DR: In this paper , the authors considered the Brézis-Nirenberg problem with the Choquard equations and showed that, for each λ>0, this problem has infinitely many solutions by using truncation method.
References
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Journal ArticleDOI
The Brezis-Nirenberg result for the fractional Laplacian
TL;DR: In this paper, the authors studied the non-local fractional version of the Laplace equation with critical non-linearities and derived a Brezis-Nirenberg type result.
Journal ArticleDOI
Theory of Electrical Breakdown in Ionic Crystals
TL;DR: In this article, the critical field strength at which the breakdown occurs has been calculated in the following way: in strong external electrical fields, there are always some electrons in the conduction levels of an ionic crystal.
Journal ArticleDOI
A guide to the Choquard equation
TL;DR: A survey of the existence and properties of solutions to the Choquard type equations can be found in this paper, where some variants and extensions of its variants can also be found.
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Existence of groundstates for a class of nonlinear Choquard equations
TL;DR: In this article, the authors prove the existence of a nontrivial solution to the nonlinear Choquard equation in ℝ^N, where I_α is a Riesz potential.
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Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems
TL;DR: In this article, it was shown that several minimax principles of the Ambrosetti-Rabinowitz type remain valid for functions satisfying (H) and (PS), and may therefore be used to prove the existence of critical points other than local minima.