The Existence Of Solutions To Two Types Of Nonlinear Elliptic Equations

This paper is divided into the following two parts:1.Consider the following second order Hamiltonian systems:(?)-L(t)u + Wu(t,u)= 0,t ∈ R(HS) to obtain the existence and multiplicity of homolysis.where t ∈ R,L(t)∈ C(R,Rn×n)is a symmetric positive definite matrix,W(t,u)?satisfies the super quadratic condition.By making some reasonable assumptions about L and W,we can use the fountain theorem to prove that the existence of system(HS)is infinite nontrivial homolysis.2.Consider the following equation:(?)For V and f to make some more relaxed assumptions,we have verified the existence and multiplicity of equation solutions in the absence of compactness embedded in the working space.To ensure that there is at last one or more nontrivial solutions to the above problems,we need to apply the critical point theory.