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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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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: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 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, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$ where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$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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한국수학교육학회지시리즈B:순수및응용수학

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