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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

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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (DEPARTMENT OF APPLIED MATHEMATICS, BEIJING INSTITUTE OF TECHNOLOGY)
Ge, Weigao (DEPARTMENT OF APPLIED MATHEMATICS, BEIJING INSTITUTE OF TECHNOLOGY)
Yang, Aijun, & Ge, Weigao. (2008). POSITIVE SOLUTIONS OF SELF-ADJOINT BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS AT RESONANCE. 한국수학교육학회지시리즈B:순수및응용수학, 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

한국수학교육학회지시리즈B:순수및응용수학

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