The Existence Of Solutions For Several Classes Of Elliptic Equations With Non-local Terms

In this paper,we apply critical point theory to study two kinds of nonlocal elliptic partial differential equations aiming to establish the existence of ground state solutions,positive solutions and sign-changing solutions of those systems.Under the assumption of this article,The nonlinear term f is only required to be continuous,so that the Nehari manifold does not have to be C1.In the second chapter,we study the existence of nontrivial solutions for Kirchhoff equations with periodic potentials.Where f satisfies a more general 4-superlinear condition but not need to be C1.Under the assumptions on f which may subcritical or critical growth at infinity,by using the generalized Nehari manifold method of Szulkin and Weth,we prove the existence of ground state solutions.At last,when the potential V(x)is constant,we prove the existence of the ground state solution of the autonomous Kirchhoff type equation.In the third chapter,we study the existence of positive solutions for a class of Schrodinger-Poisson equations with critical growth exponential.Where f satisfies subcritical growth condition,the potential V vanish at infinity.Using the variational method,we prove that there exists positive solution.In the fourth chapter,we study the existence of sign changing solutions for a class of p-Laplacian Kirchhoff equation with potential vanishing at infinity.Where f is not C1 function,Using a minimization argument and the Nehari manifold method,we prove the existence of a least energy sign changing solution to this problem.Further,when f is an odd function,we prove that there are infinitely many nontrivial solutions.