Existence of Multiple Solutions for Certain Quasilinear Elliptic Problems Under Flux Boundary Conditions

Ahmed Ahmed, Taghi Ahmedatt and Yongqiang Fu

Journal of Mathematics, 2024, vol. 2024, 1-19

Abstract: In this paper, we consider the following quasilinear p⟶⋅-elliptic problems with flux boundary conditions of the type −∑i=1N∂/∂xiaix,∂u/∂xi+bxupMx−2u=f1x,u−sgnug1x in Ω,∑i=1Naix,∂u/∂xiνi=cxuqx−2u+f2x,u−sgnug2x on ∂Ω.. Using the Fountain theorem and dual Fountain theorem, we prove the existence and multiplicity of solutions for a given problem, subject to different hypotheses. Specifically, this problem has already been resolved within the anisotropic variable exponent Sobolev space W1,p⟶⋅Ω, with the aforementioned tools serving as the primary techniques. By employing these methods, we demonstrate that the problem has solutions that can take on multiple forms, depending on the underlying assumptions.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6647045

DOI: 10.1155/jom/6647045

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