The Study On Boundary Problems For A Class Of Nonlinear Elliptic Equation (System)

By the methods of Green function, fixed point in a cone, Galerkin and upper and lower solutions in this paper, we deal with existence and non-existence of solutions to a class of nonlocal elliptic equation(systems) in a bounded domain and R~N, further more; and by the method of Schauder fixed point, we obtain existence of solution to a class of (p,q)-Laplacian elliptic systems, at the same time we prove the solutions converges to positive constant or with specific order of growth in the infinity; at last, we study existence and non-existence of nonnegative boundary blow-up entire solutions to a class of m-Laplacian equation.The main content of this paper is divided into five chapters:In chapter two, we discuss existence of solution to the following nonlocal elliptic equation with the third boundary value:(1)where In chapter three, we discuss existence of solution to the following nonlocal elliptic equation in R~N:(2)Then discuss non-existence of solution to the following nonlocal elliptic equations(3)Where Ω is a smooth bounded domain of R~N, N ≥ 2, a, b are positive continuous functions and f(x, v), g(x, u) satisfy Caratheodory conditions in Ω ×R.