Positive solutions for nonlinear Choquard equation with singular nonlinearity
TLDR
In this article, the existence and multiplicity of positive weak solutions of the Choquard equation with singular non-linearity was studied and the regularity of these weak solutions was studied.Abstract:
In this article, we study the following non-linear Choquard equation with singular non-linearitywhere is a bounded domain in with smooth boundary , and . Using variational approach and structure of associated Nehari manifold, we show the existence and multiplicity of positive weak solutions of the above problem, if is less than some positive constant. We also study the regularity of these weak solutions.read more
Citations
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Variable order nonlocal Choquard problem with variable exponents
Reshmi Biswas,Sweta Tiwari +1 more
TL;DR: In this article, the existence/multiplicity results for the variable order nonlocal Choquard problem with variable exponents were studied and the existence and multiplicity results were derived.
Book ChapterDOI
Critical Growth Elliptic Problems with Choquard Type Nonlinearity: A Survey
TL;DR: A survey of recent developments and results on Choquard equations is given in this article, where the authors focus on the existence and multiplicity of solutions of the partial differential equations which involves the nonlinearity of the convolution type.
Journal ArticleDOI
Nonlocal perturbations of the fractional Choquard equation
TL;DR: In this paper, the existence of least energy sign-changing solutions by considering the Nehari nodal set is investigated by using a minimization method on the associated Nehari manifold, where the groundstate solutions are obtained by using the minimum energy sign changing solution.
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Variable order nonlocal Choquard problem with variable exponents
Reshmi Biswas,Sweta Tiwari +1 more
TL;DR: In this article, the existence/multiplicity results for the variable order nonlocal Choquard problem with variable exponents were studied under the Hardy-Sobolev-Littlewood-type result for the fractional Sobolev space.
Journal ArticleDOI
On concentration of least energy solutions for magnetic critical Choquard equations
TL;DR: In this article, the authors considered the magnetic nonlinear Choquard equation and established the existence of least energy solution under some suitable conditions, where the concentration behavior of solutions is studied as μ → + ∞.
References
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Positive solutions for singular nonlinear elliptic equations
TL;DR: In this article, singular semilinear elliptic equations in bounded domains with Dirichlet boundary data are dealt with, and the existence, uniqueness and linearized stability of positive solutions for a series of nonlinear eigenvalue problems are investigated.
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Fractional Choquard equation with critical nonlinearities
TL;DR: In this paper, the Brezis-Nirenberg type problem of nonlinear Choquard equation involving the fractional Laplacian was studied and some existence, nonexistence and regularity results for weak solution of the above problem using variational methods were obtained.
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The Nehari manifold for a semilinear elliptic equation involving a sublinear term
TL;DR: In this article, the relation between the Nehari manifold and fibrering maps was explored and the results on bifurcation from infinity were linked to results on results associated with the problem.
Journal ArticleDOI
Multiplicity Results for a Semi-Linear Elliptic Equation Involving Sign-Changing Weight Function
TL;DR: In this article, the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic equation with sign-changing weight functions was studied.
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