In this paper, we consider a class of singular elliptic equation on bounded domain. By the variational method, we prove the existence of solutions.

In this paper, we study the existence of solutions for a class of elliptic equation. By the variational methods, we give the sufficient conditions that insure the existence of solutions.

In this paper, a class of elliptic equation with convex-concave nonlinear term is considered. By the variational methods, we give a sufficient condition which insures that the problem considered in the present paper has at a nontrivial nonnegative solution.

By the method of up-sub solutions, we consider a class of parabolic equations with nonlocal source. In the paper, we discuss the relation of the coefficients and the importance of the initial value. We get the sufficient conditions for the global existence and finite blow-up of the solutions.

We establish a fixed point theorem in the generalized metric space introduced by M.oradi and Beiranvand for mapping satisfying a general contractive inequality. The obtained result can be considered as an extension of the theorem of Moradi and Beiranvand.