Multiple solutions of impulsive Sturm-Liouville boundary value problem via lower and upper solutions and variational methods

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:387

Article

Tian, Yu¹  Ge, Weigao² 

[1] Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China

[2] Beijing Inst Technol, Dept Appl Math, Beijing 100081, Peoples R China

关键词: Multiple solutions;    Impulsive Sturm-Liouville boundary value problem;    Critical point;    Lower and upper solutions;    Variational methods;   

DOI  :  10.1016/j.jmaa.2011.08.042

来源: Elsevier

【 摘 要 】

In this paper, we prove the existence of multiple solutions for second order Sturm-Liouville boundary value problem {-Lu = f(x, u), x is an element of [0,1]\[x(1), x(2), ... , x(1)], -Delta(p(x(i))u'(x(i))) = l(i)(u(x(i))), i = 1,2, ... , l, R-1(u) = 0, R-2(u) = 0, where Lu = (p(x)u')' - q(x)u is a Sturm-Liouville operator, R-1(u) = alpha u'(0) - beta u(0), R-2(u) = gamma u'(1)+sigma u(1). The technical approach is fully based on lower and upper solutions and variational methods. The interesting point is that the property that the critical points of the energy functional are exactly the fixed points of an operator that involves the Green's function. Besides, the existence of four solutions is given. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free