Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations
نویسندگان
چکیده
منابع مشابه
Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations
In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fourth-order differential equations. The notions of classical and weak solutions are introduced. Then the existence of at least one and infinitely many nonzero solutions is proved, using the minimization, the mountain-pass, and Clarke's theorems.
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متن کاملExistence and Multiplicity of Solutions to a Boundary Value Problem for Impulsive Differential Equations
Chunyan He, Yongzhi Liao, and Yongkun Li 1 Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China 2 School of Mathematics and Computer Science, Panzhihua University, Panzhihua, Sichuan 617000, China Correspondence should be addressed to Yongkun Li; [email protected] Received 24 October 2012; Revised 20 December 2012; Accepted 21 December 2012 Academic Editor: Wan-Tong Li Cop...
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in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime...
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ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2014
ISSN: 1687-2770
DOI: 10.1186/1687-2770-2014-105