Existence of a non-trivial solution for the image-Laplacian equation with Fučík-type resonance at infinity, III Original Research Article

We prove the existence of a non-trivial weak solution for the pp-Laplacian equation View the MathML source{−Δpu=g(x,u)inΩ,u=0on∂Ω, Turn MathJax on by variational methods. We treat mainly the case of a nonlinear term gg satisfying the following conditions for some constants a0a0, b0b0, aa and bb: View the MathML sourceg(x,u)={a0u+p−1−b0u−p−1+o(∣u∣p−1)at0,au+p−1−bu−p−1+o(∣u∣p−1)at∞. Turn MathJax on We consider the resonant case in the sense that (a,b)(a,b) belongs to the Fučík spectrum for the pp-Laplacian.