Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations

Authors:	John R. Graef Chuanxi Qian Bo Yang

Affiliation:	Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403 ; Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762 ; Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762

Abstract:	In this paper, the authors consider the boundary value problem $begin{displaymath}({E}) qquadqquadquad x^{(2m)}(t)+(-1)^{m+1} f(x(t))=0, quad 0<t<1, qquadqquadquad, end{displaymath}$ $begin{displaymath}({B}) qquadqquad x^{(2i)}(0)=x^{(2i)}(1)=0, quad i=0,1,2,cdots,m-1, qquadqquad end{displaymath}$ and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)-(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373-2379) are discussed.

Keywords:	Boundary value problems existence of positive solutions higher order equations multiple solutions nonlinear equations

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