Multiple positive solutions of nonlinear $m$-point dynamic equations for $p$-Laplacian on time scales

Authors : Abdülkadir DOĞAN

Pages : 941-959

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we study the existence of positive solutions of a nonlinear $ m $-point $p$-Laplacian dynamic equation $$insert ignore into journalissuearticles values(\phi_pinsert ignore into journalissuearticles values(x^\Deltainsert ignore into journalissuearticles values(t);););^\nabla+winsert ignore into journalissuearticles values(t);finsert ignore into journalissuearticles values(t,xinsert ignore into journalissuearticles values(t);,x^\Deltainsert ignore into journalissuearticles values(t););=0,\hspace{2cm} t_1< t 1.$ Sufficient conditions for the existence of at least three positive solutions of the problem are obtained by using a fixed point theorem. The interesting point is the nonlinear term $f$ is involved with the first order derivative explicitly. As an application, an example is given to illustrate the result.
Keywords : Time scales, boundary value problem, p Laplacian, positive solutions, fixed point theorem