Three positive solutions for p-Laplacian functional dynamic equations on time scales

W. Guan, Lanzhou University of Technology, Lanzhou, Gansu, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 28. (2008), pp. 1-7.

Abstract: In this paper, existence criteria of three positive solutions to the followimg $p$-Laplacian functional dynamic equation on time scales

\[\left\{\begin{array}{l}
\left[ \Phi _p(u^{\bigtriangleup }(t))\right] ^{\bigtriangledown}+a(t)f(u(t),u(\mu (t)))=0,t\in \left(0,T\right),\\
u_0(t)=\varphi (t), t\in \left[ -r,0\right], u(0)-B_0(u^{\bigtriangleup }(\eta ))=0, u^{\bigtriangleup }(T)=0,
\end{array}\right.\]

are established by using the well-known Five Functionals Fixed Point Theorem.

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