Abstract:

This paper is concerned with the p-Laplacian boundary value problem (g(u^△(t)))^▽+a(t)f(t, u(t))=0 for t ∈ [ 0, T]_T, u(0)=u(T)=w, u^△(0)=-u^△(T), where w is a
nonnegative real number and g(ν)=lν|^p-2ν with p>1 . By using symmetry technique and a five functionals fixed-point theorem, we prove that the boundary value problem has at least three positive symmetric solutions. As application, an example is given to illustrate our result.

Key words: Time scales, Boundary value problem, Positive symmetric solution, p-Laplacian, Fixed point theorem