Multiplicity results for the (p(x),q(x))−Kirchhoff equations

Azhar Saeed, Mohsen Alimohammady, Asieh Rezvani

Abstract


We study the existence and multiplicity of weak solutions for the following equation involving variable exponents:  −△k˜p p(x) u(x) − △k˜q q(x) u(x) + |u| p(x)−2u + |u| q(x)−2u = λf(x, u(x)), in Ω, u = 0 on ∂Ω, where Ω is a bounded domain of RN with smooth enough boundary which is subject to Dirichlet boundary condition, λ is a positive real parameter and p is real continuous function on Ω¯. Using a variational method, we would show the existence and multiplicity of the solutions. To this purpose, we would focus on a generalized variable exponent Lebesgue- Sobolev space.

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DOI: https://doi.org/10.52846/ami.v52i2.1950