The multiple positive solutions for p-Laplacian multipoint BVP with sign changing nonlinearity on time scales

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:344

Article

Zhu, Yunzhou^1,2  Zhu, Jiang¹ 

[1] Xuzhou Normal Univ, Sch Math Sci, Xuzhou 221116, Peoples R China

[2] Xuzhou Higher Normal Sch, Xuzhou 221116, Peoples R China

关键词: time scales;    p-Laplacian;    positive solutions;    fixed point index;    cone;   

DOI  :  10.1016/j.jmaa.2008.02.032

来源: Elsevier

【 摘 要 】

In this paper, we consider the following p-Laplacian multipoint boundary value problem on time scales: (phi(p) (u(Delta)(t)))(del) + a(t) f (t, u(t)) = 0, t is an element of [0, T](T), phi(P) (u(Delta)(0)) = (n-2)Sigma(i=1)a(i)phi(p)(u(Delta)(xi(i))), u(T) = (n-2)Sigma(i=1)b(i)u(xi(i)), where phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1, xi(i) is an element of [0, T](T), 0 < xi(1) < xi(2) < ... < xi(n-2) < rho(T). By using fixed point index, we provide some sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. Especially, the nonlinear term f(t, u) is allowed to change sign. As an application, an example is given to demonstrate our result. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free