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Full-Text Articles in Physical Sciences and Mathematics
New Oscillation Tests And Some Refinements For First-Order Delay Dynamic Equations, Başak Karpuz, Özkan Öcalan
New Oscillation Tests And Some Refinements For First-Order Delay Dynamic Equations, Başak Karpuz, Özkan Öcalan
Turkish Journal of Mathematics
In this paper, we present new sufficient conditions for the oscillation of first-order delay dynamic equations on time scales. We also present some examples to which none of the previous results in the literature can apply.
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
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.