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ISSN : 1226-0657

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Vol.17 No.1

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SOLVABILITY FOR SECOND-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS ON AN UNBOUNDED DOMAIN AT RESONANCE

SOLVABILITY FOR SECOND-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS ON AN UNBOUNDED DOMAIN 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
2010, v.17 no.1, pp.39-49
Yang, Ai-Jun (COLLEGE OF SCIENCE, ZHEJIANG UNIVERSITY OF TECHNOLOGY)
Wang, Lisheng (SCHOOL OF MATHEMATICS AND PHYSICS, JINGGANGSHAN UNIVERSITY)
Ge, Weigao (DEPARTMENT OF APPLIED MATHEMATICS, BEIJING INSTITUTE OF TECHNOLOGY)
Yang, Ai-Jun, Wang, Lisheng, & Ge, Weigao. (2010). SOLVABILITY FOR SECOND-ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS ON AN UNBOUNDED DOMAIN AT RESONANCE. 한국수학교육학회지시리즈B:순수및응용수학, 17(1), 39-49.

Abstract

This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, <TEX>$\infty$</TEX>) with the boundary conditions <TEX>$$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$</TEX> where <TEX>$g\;{\in}\;L^1[0,{\infty})$</TEX> with g(t) > 0 on [0, <TEX>$\infty$</TEX>) and <TEX>${\int}^{\infty}_0g(s)ds\;=\;1$</TEX>, f is a g-Carath<TEX>$\acute{e}$</TEX>odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.

keywords
integral boundary condition, unbounded domain, g-Carath<tex> $\acute{e}$</tex>odory function, resonance

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