Bifurcation techniques for a class of boundary value problems of fractional impulsive differential equations

Liu, Yansheng¹

¹ Department of Mathematics, Shandong Normal University, Jinan, 250014, P. R. China

Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 4, p. 340-353.

Résumé

This paper investigates the existence of positive solutions for a class of boundary value problems (BVP) of fractional impulsive differential equations and presents a number of new results. First, by constructing a novel transformation, the considered impulsive system is convert into a continuous system. Second, using a specially constructed cone, the Krein-Rutman theorem, topological degree theory, and bifurcation techniques, some sufficient conditions are obtained for the existence of positive solutions to the considered BVP. Finally, an example is worked out to demonstrate the main result.

Détail

DOI : 10.22436/jnsa.008.04.07

Classification : 34A60, 34B16, 34B18
Keywords: Positive solutions, bifurcation techniques, fractional differential equations with impulse, boundary value problems.

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