Existence And Uniqueness Of Solution For Mixed Type Nonlinear Elliptic Systems Of Second Order

In this paper, the second order nonlinear elliptic systemwith α < 1, β ≥ 1 and 0 < γ < 1 is considered in Ω, which is a bounded open subset of R~N, N ≥ 3. Under a set of suitable hypotheses on function f_i, Q_i, h_i and P, it is shown that this system possesses a positive solution (u,v) ∈The paper is mainly divided into four sections.In the fisrt section, we give an introduction of this paper. It includes the background of this problem, the main work in this paper and some open problems.Next, we provide some basal definitions and theories in the second section, such as the maximum principle, Holder continuity, Schauder theory and so on, which are foundation of the later work.The third section of this paper solves the existence and uniqueness of the positive entire solutions to a certain second order nonlinear elliptic equation. To solve this problem, upper and lower method and comparison lemma are introduced.At last, we establish the main theorem of this paper, the existence and uniqueness of positive solutions for system (*).