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

Authors: ABDÜLKADİR DOĞAN

Abstract: In this paper, we study the existence of positive solutions of a nonlinear $ m $-point $p$-Laplacian dynamic equation $$(\phi_p(x^\Delta(t)))^\nabla+w(t)f(t,x(t),x^\Delta(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

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