The Nontrivial Solutions Of Some Superlinear Equations

The main objective is to study Minimax theory and Morse theory in the modern critical point theory. Mountain pass lemma by Ambrosetti-Rabinowitz can be said is an important milestone in development history of critical point theory. Linking theorem further promote the mountain Theorem. We study the existence and multiplicity of nontrivial solution for Semilinear elliptic equations.The paper is concerned with a superlinear Robin boundary value problem and Hamilton system problem. We study the existence of nontrivial solutions for them, by using Local linking theory and fountain theorem, and obtain some new results.The thesis is divided into four sections according to contents.Chapter1Preference, we introduce the main contents of this paper.Chapter2In Chapter2, we are interested in existence of a nontrivial solutions for a class of semilinear elliptic equations with a Robin boundary value condition Where Ω∈RN(N≥3) is a bounded domain with a piecewise smooth boundary a∈L∞(Ω),0≤b∈L∞((?)Ω).Chapter3In Chapter3, we are interested in Hamilton system with infinitely many periodic solution Where T>0, F:R×RNâ†'R, and F on the x with T Cycle.