Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations

By Xiaoning Lin, Daqing Jiang. 2006

149 citations recorded by the source corpus.

Abstract This paper is devoted to study the existence of multiple positive solutions for the second order Dirichlet boundary value problem with impulse effects. The main results here is the generalization of Liu and Li [L. Liu, F.Y. Li, Multiple positive solution of nonlinear two-point boundary value problems, J. Math. Anal. Appl. 203 (1996) 610–625] for ordinary differential equations. Existence is established via the theory of fixed point index in cones.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c42bbf7727f0bf9d6c26c20f93c86f227879c7a6

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In Applied Mathematics

1. Yu Tian
2. Weigao Ge

In Numerical Analysis

1. Yu Tian
2. Weigao Ge

Citations in the corpus

• Positive solutions for second order impulsive differential equations with integral boundary conditions (2011, unknown): “Recently, Lin and Jiang [15] studied the second order impulse boundary value problem x00ðtÞ 1⁄4 f ðt; xÞ; t–tk; t 2 ð0;1Þ; Dxjt1⁄4tk 1⁄4 IkðxðtkÞÞ; k 1⁄4 1;2; .”
• APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS (2008, methodology): “These classical tools include fixed-point theorems in cones [1,9,11,14] and the method of lower and upper solutions with monotone iterative technique (see [15]).”