Existence of solutions for a nonhomogeneous Dirichlet problem involving 𝑝(𝑥)-Laplacian operator and indefinite weight
Published in Boundary Value Problems
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: −Δ𝑝(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 variab...
We show the existence of a first curve in the Fučik spectrum with weights for the p-Laplacian under mixed boundary conditions. We also study the asymptotic behavior of this first curve.