Research On Several Elliptic Equations With Asymptotically Linear

In this paper,we are concerned with the existence of solutions for a few class of semilinear elliptic equations or semilinear elliptic systems with asymptotically property at infinity.At first chapter we introduce the relevant bakeground knowledge and prepared.At second chapter we concider the singular semilinear elliptic equations invoving Hardy potential of the formWhen the nonlinearity f(u) is asymptotically,by using Mountain pass theorem,we prove the existence of nontrivial solutions of the equations(0-1) in R~N.At third chapter we study the semilinear elliptic system with parameters of the formwhere is smooth bounded domain, N ≥3,λ and u are nonnegative numbers.When our nonlinearities doesn’t satisfy non-decreasing condition,we prove the elliptic system(0-2) has at least one nontrivial solutions if λμ >1 and λ .At fourth chapter we concider the semilinear elliptic system:where λμ >1, λ >l +1 and m >μ +1.From Sobolev compact embedding theorem we konw H_r~1(R~N)L_r~1(R~N),then we use variational techniques to discuss the existence of nontrivial solutions to the problem in H_r~1(R~N).