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

Graef, John; Qian, Chuanxi; Yang, Bo

doi:10.1090/S0002-9939-02-06579-6

Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations
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by John R. Graef, Chuanxi Qian and Bo Yang PDF

Proc. Amer. Math. Soc. 131 (2003), 577-585 Request permission

Abstract:

In this paper, the authors consider the boundary value problem \begin{gather} \tag {E} x^{(2m)}(t)+(-1)^{m+1} f(x(t))=0, \quad 0<t<1, \\ \tag {B} x^{(2i)}(0)=x^{(2i)}(1)=0, \quad i=0,1,2,\cdots ,m-1, \end{gather} 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.

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