Browsing by Author "Abdou, Aboubacar"

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    Existence of solutions for a nonhomogeneous Dirichlet problem
    (Springer Open, 2019) Marcos, Aboubacar; Abdou, Aboubacar
    We obtain multiplicity and uniqueness results in the weak sense for the following nonhomogeneous quasilinear equation involving the p(x)-Laplacian operator with Dirichlet boundary condition: – p(x)u + V(x)|u| q(x)–2u = f(x, u) in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in RN, V is a given function with an indefinite sign in a suitable variable exponent Lebesgue space, f(x,t) is a Carathéodory function satisfying some growth conditions. Depending on the assumptions, the solutions set may consist of a bounded infinite sequence of solutions or a unique one. Our technique is based on a symmetric version of the mountain pass theorem.