Gurdev C. Anthal | Searcharxiv

arXiv2023

An elliptic problem involving critical Choquard and singular discontinuous nonlinearity

The present article investigates the existence, multiplicity and regularity of weak solutions of problems involving a combination of critical Hartree type nonlinearity along with singular and discontinuous nonlinearity. By applying variational methods and using the notion of generalized gradients for Lipschitz continuous functional, we obtain the existence and the multiplicity of weak solutions for some suitable range of $λ$ and $γ$. Finally by studying the $L^\infty$-estimates and boundary behavior of weak solutions, we prove their Hölder and Sobolev regularity.

math.AP↗

arXiv2022

Choquard equation involving mixed local and nonlocal operators

In this article, we study an elliptic problem involving an operator of mixed order with both local and nonlocal aspects and in the presence of critical nonlinearity of Hartree type. To this end, we first investigate the corresponding Hardy-Littlewood-Sobolev inequality and detect the optimal constant. Using variational methods and a Pohožaev identity we then show the existence and nonexistence results for the corresponding subcritical perturbation problem.

math.AP↗