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Abstract In this paper, we study the existence of multiple positive solutions for boundary value problems of high-order Riemann–Liouville fractional differential equations involving the p-Laplacian operator. Not only new existence conclusions of two positive solutions are obtained by employing functional-type cone expansion-compression fixed point theorem, but also some sufficient conditions for existence of at least three positive solutions are established by applying the Leggett–Williams fixed point theorem. In addition, we demonstrate the effectiveness of the main result by using an example.

In this paper, we study the existence of multiple positive solutions for boundary value problems of high-order Riemann–Liouville fractional differential equations involving the p-Laplacian operator. Not only new existence conclusions of two positive solutions are obtained by employing functional-type cone expansion-compression fixed point theorem, but also some sufficient conditions for existence of at least three positive solutions are established by applying the Leggett–Williams fixed point theorem. In addition, we demonstrate the effectiveness of the main result by using an example. [ABSTRACT FROM AUTHOR]

By using Leggett-Williams fixed point theorem and Hölders inequality, the existence of three positive solutions for the fourth-order impulsive differential equations with integral boundary conditions x(4)(t) = (t)f(t,x(t)), 0 < t < 1, t ≠ tk, Δx|t=tk = Ik(tk, x(tk)), Δx'|t=tk = 0, k = 1,2,..., m, x(0) = ∫0¹ g(s)x(s)ds, x'(1) = 0, x''(0) = ∫0¹ = h(s)x''(s) ds, x'''(1) = 0 is considered, where (t) is Lp-integrable. Our results cover a fourth-order boundary value problem without impulsive effects and are compared with some recent results. [ABSTRACT FROM AUTHOR]