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  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.21 No.3

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EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2014, v.21 no.3, pp.147-163
https://doi.org/10.7468/jksmeb.2014.21.3.147
Miao, Chunmei (School of Mathematics and Statistics, Northeast Normal University)
Ge, Weigao (School of Mathematics, Beijing Institute of Technology)
Zhang, Zhaojun (School of Science, Changchun University)
Miao, Chunmei, Ge, Weigao, & Zhang, Zhaojun. (2014). EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS. 한국수학교육학회지시리즈B:순수및응용수학, 21(3), 147-163, https://doi.org/10.7468/jksmeb.2014.21.3.147

Abstract

In this paper, we study the existence of positive solutions for singular impulsive differential equations with integral boundary conditions <TEX>$$\{u^{{\prime}{\prime}}(t)+q(t)f(t,u(t),u^{\prime}(t))=0,\;t{\in}\mathbb{J}^{\prime},\\{\Delta}u(t_k)=I_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\{\Delta}u^{\prime}(t_k)=-L_k(u(t_k),u^{\prime}(t_k)),\;k=1,2,{\cdots},p,\\u=(0)={\int}_{0}^{1}g(t)u(t)dt,\;u^{\prime}=0,$$</TEX>) where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based on the theory of Leray-Schauder degree, together with a truncation technique. Some recent results in the literature are generalized and improved.

keywords
singular impulsive diffrential equations, integral boundary conditions, positive solutions, Leray-Schauder degree

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한국수학교육학회지시리즈B:순수및응용수학

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