The uniqueness of solution for a fractional order nonlinear eigenvalue problem with p-Laplacian operator

作者：Yang, Ge-Feng^*; Zhong, Minling

来源：Advances in Difference Equations, 2014, 2014(1): 186.

DOI：10.1186/1687-1847-2014-186

• eigenvalue problem
• uniqueness
• p-Laplacian operator
• fractional differential equation

In this article, we investigate the uniqueness of solutions for the fractional order differential equation with p-Laplacian operator - XDt alpha (phi(beta)(t) X))(t) = lambda f(t, x(t)), t epsilon (0, x(0) =0, D-t(beta) X(0) = 0, D-t(gamma) (1) = Sigma(m-2)(j=1) a(j)D(t)(gamma) X(xi(j)), where D-t(alpha), D-t(beta), D-t(gamma) are the standard Riemann-Liouville derivatives with 1 < beta <= 2,0 < gamma <= beta - gamma - 1 < xi(1) < xi(2) < ... < xi(p-2) < 1, a(j) epsilon [0, +infinity) with c = Sigma(m-2)(j-1) a(j)xi(beta-gamma-1)(j) < 1, and the p-Laplacian operator is defined as phi(p)(s) = vertical bar s vertical bar(p- 2)s, p > 1. Based on a basic property of the p- Laplacian operator and the Banach contraction mapping principle, the uniqueness of solutions for the fractional order differential equation is established for the cases p > 2 and 1 < p <= 2.

• 出版日期2014-7-22
• 单位广东外语外贸大学