Multiple solutions for a nonhomogeneous Dirichlet problem in Orlicz-Sobolev spaces
Abstract In this paper, moving within the framework of Orlicz–Sobolev spaces, we guarantee through variational arguments the existence of three weak solutions to the nonhomogeneous boundary value problem: - div ( a ( | ∇ u ( x ) | ) ∇ u ( x ) ) = λ f ( x , u ) + μ g ( x , u ) in Ω , u = 0 on ∂ Ω , with Ω bounded domain in R n with smooth boundary ∂ Ω , λ , μ real parameters, f , g : Ω × R → R Caratheodory functions and the function t → a ( | t | ) t odd, increasing homeomorphism from R onto R . Applications and comparisons are also presented; in particular, we improve a result for an eigenvalue problem established by Mihăilescu and Repovs in [15] .