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ISSN : 1226-0657

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Vol.15 No.4

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POSITIVE SOLUTIONS OF SELF-ADJOINT BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2008, v.15 no.4, pp.407-414
Yang, Aijun
Ge, Weigao
Yang,, A. , & Ge,, W. (2008). POSITIVE SOLUTIONS OF SELF-ADJOINT BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 15(4), 407-414.

Abstract

In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x'(t))'+f(t,x(t))=0, t <TEX>$${\in}$$</TEX> (0,1), x'(0)=0, x(1) = <TEX>$${\int}_0^1$$</TEX> x(s)g(s)ds. A new result on the existence of positive solutions is obtained. The interesting points are: the first, we employ a new tool-the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.

keywords
boundary value problem, resonance, cone, positive solution, coincidence

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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