Existence of Non-Trivial Solutions for p-Laplacian Problems in the Non-Resonant and Resonant Cases with Respect To FucIK Spectrum

摘要

We prove the existence of a non-trivial weak solution for the p-Laplacian equation-△pu=f(x,u) in Ω, u=0 on(e)Ω, by variational methods. We treat mainly the case of the term f satisfying the following conditions for L'(Ω) functions a0, b0.a and b: f(x,u)={a0(x)u+p-1-b0(x)u_p-1+o(|u|p-1) at 0, a(x)u+p-1-b (x)u_p-1+o(|u|p-1)at ∞.