Research On The Existence Of Positive Solutions Of Boundary Value Problems For Differential Equations

At Chapter 2 of this paper, by using fixed point theorem in cone ,we discuss the existence of positive solutions of three-order three-point boundary value problems(1.3) where,is continuous functions. we proofTheorem 2.1 If one of the following conditions(1) , or(2), holds, then (1.3) have positive solutions.At Chapter 3, by using Leray-Schauder fixed theorem ,we discuss the existence of positive solutions of three-order singular differential equation (3.1) where , are positive constants. We proofTheorem 3.1 Assumeand satisfy:(H1)is non-negatively continuous function, 0;: is non-negatively continuous function and ;(H2); then there exists ,if , (3.1) have positive solutions. Furthermore, supposealso satisfies (H3): is monotone increasing function ,and there exists such that, then there exists ,if , (3.1) have positive solutions. if holds, (3.1)has no positive solution.Theorem 3.2 Ifandsatisfy (H1),(H2),is monotone (or positive),we suppose is one positive solution of (3.1) ,then ;On the contrary, supposeandsatisfy (H1),is monotone(or positive),and there exists some such that BVP(3.1) have positive solutions which satisfy (*),then satisfies (H2).At Chapter 4 , a new fixed point theorem is applied to obtain the existence of positive solutions of second order periodic boundary value problems (4.1) we proof ,If satisfy one of the following conditions ,then (4.1)has at least one positive solution.(F1),(F2),or(C1),(C2),...