most citedQuasilinear elliptic problem without Ambrosetti-Rabinowitz condition involving a potential in Musielak-Sobolev spaces setting

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math.AP2019★ 1 cited

Quasilinear elliptic problem without Ambrosetti-Rabinowitz condition involving a potential in Musielak-Sobolev spaces setting

Soufiane Maatouk, Abderrahmane El Hachimi

In this paper, we consider the following quasilinear elliptic problem with potential $$(P) \begin{cases} -\mbox{div}(ϕ(x,|\nabla u|)\nabla u)+ V(x)|u|^{q(x)-2}u= f(x,u) & \ \ \mbox…

math.AP2017★ 1 cited

Multiplicity of solutions for a class of elliptic problem of -Laplacian type with a -Gradient term

Zakariya Chaouai, Soufiane Maatouk

We consider the following problem $$(P) \begin{cases} -Δ_{p}u= c(x)|u|^{q-1}u+μ|\nabla u|^{p}+h(x) & \ \ \mbox{ in }Ω, u=0 & \ \ \mbox{ on } \partialΩ, \end{cases}$$ where is a…