Abstract
We investigate the existence of multiple positive solutions of fractional differential equations with p-Laplacian operator D-a+(beta)(phi(p)(D(a+)(alpha)u(t))) = f (t,u(t)), a < t < b, u((j))(a) = 0, j = 0, 1, 2, ... ,n - 2, u((alpha 1))(b) = xi u((alpha 1))(eta), phi p(D-a+(alpha) + u(a)) = 0 = D-a+(beta)(phi(p)(D(a+)(alpha)u(b))) , where beta epsilon (1,2], alpha epsilon (n - 1, n], n >= 3, xi epsilon (0, infinity), eta epsilon (a, b), beta(1) epsilon (0, 1], alpha(1) epsilon {1, 2,..., alpha - 2} is a fixed integer, and phi(p)(s) = vertical bar s vertical bar(p-2)s, p > 1, phi(-1)(p) = phi(q), (1/p) + (1/q) = 1, by applying Leggett-Williams fixed point theorems and fixed point index theory.