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math.AP2022★ 2 cited
An existence result for -Laplace equation with gradient nonlinearity in
Shilpa Gupta, Gaurav Dwivedi
We prove the existence of a weak solution to the problem \begin{equation*} \begin{split} -Δ_{p}u+V(x)|u|^{p-2}u & =f(u,|\nabla u|^{p-2}\nabla u), \ \ \ \\ u(x) & >0\ \ \forall x\in…
math.AP2022★ 12 cited
Kirchhoff type elliptic equations with double criticality in Musielak-Sobolev spaces
Shilpa Gupta, Gaurav Dwivedi
This paper aims to establish the existence of a weak solution for the non-local problem: \begin{equation*} \left\{\begin{array}{ll} -a\left(\int_Ω\mathcal{H}(x,|\nabla u|)dx \right…