Positive Solutions Of Elliptic Equations With Nonlinear Boundary Conditions

In this thesis, the existence of positive solutions of superlinear case and asymptotically linear case of equation with nonlinear boundary value condition is considered, where Ω is a bounded domain in R" with smooth boundary (?)Ω,(?)/(?)λ is the outer unit normal derivative.Firstly, in this thesis, the development and previous research results on superlinear case and asymptotically linear case of equation (P) are surveyed. And we offer some necessary preliminaries.Secondly, we consider superlinear case of equation (P), which f(x,u) satisfies the assumptionWe use a variant version of the Mountain Pass theorem and Ekeland’s variational principle to obtain at least two positive solutions of equation (P).Lastly, we consider asymptotically linear case of equation (P), which f(x,u) satisfies the assumption where λ1< q (x)∈L∞ (Ω), and q (x)≠+∞, (?)x∈Ω.We use a variant version of the Mountain Pass theorem and variational method to obtain at least one positive solution of equation (P).