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

• Main Author: Da-Bin Wang
• Format: Article
• Language: English
• Published: Texas State University 2007-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: Time scale; p-Laplacian functional dynamic equation; boundary value problem; positive solution; fixed point
• Online Access: http://ejde.math.txstate.edu/Volumes/2007/95/abstr.html
• ISSN: 1072-6691

In this paper, we establish the existence of three positive solutions to the following p-Laplacian functional dynamic equation on time scales, $$displaylines{ [ Phi _p(u^{Delta }(t))] ^{ abla}+a(t)f(u(t),u(mu (t)))=0,quad tin (0,T)_{mathbf{T}}, cr u_0(t)=varphi (t),quad tin [-r,0] _{mathbf{T}},\ u(0)-B_0(u^{Delta }(eta ))=0,quad u^{Delta }(T)=0,. }$$ using the fixed-point theorem due to Avery and Peterson [8]. An example is given to illustrate the main result.