Triple positive solutions of fourth-order four-point boundary value problems for -Laplacian dynamic equations on time scales.
Twin positive solutions for fourth-order two-point boundary-value problems with sign changing nonlinearities.
Twin positive solutions for three-point boundary value problems of higher-order differential equations.
Twin positive solutions of a nonlinear -point boundary value problem for third-order -Laplacian dynamic equations on time scales.
Two modifications of the Leggett-Williams fixed point theorem and their applications.
Two positive solutions for a nonlinear four-point boundary value problem with a p-Laplacian operator.
Two positive solutions for second-order functional and ordinary boundary-value problems.
Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation
We investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives....