The Existence Of Solutions Of One Elliptic Problem With P-Laplacian And An Asymptotic Linear Equation

This paper deals with the existence and multiplicity for one elliptic problems with p-Laplacian and an asymptotic linear equation by variational methods, especially the Mountain pass Lemma. In chapter 2, it is proved that there exists many solutions of the p-Laplacian equation such as -Δ_pu =λ₁ h(x)|u|^p-2u + f (x, u) by applying Morse theorem and local linking. In chapter 3, our interest switches to another situation in which the nonlinear term f ( x ,t ) is asymptotically linear in t at infinity by applying the concentration-compactness principle. The existence of the weak solution of the equation -Δu = f (x, u) is obtained.