Solvability for fractional order boundary value problems at resonance

Solvability of Nonlocal Fractional Boundary Value Problems

Solvability for Second-order M-point Boundary Value Problems at Resonance on the Half-line

In this article, we investigate the existence of positive solutions for second-order m-point boundary-value problems at resonance on the half-line (q(t)x′(t))′ = f(t, x(t), x′(t)), a.e. in (0,∞), x(0) = m−2 X i=1 αix(ξi), lim t→∞ q(t)x′(t) = 0. Some existence results are obtained by using the Mawhin’s coincidence theory.

SOLVABILITY OF FRACTIONAL MULTI-POINT BOUNDARY-VALUE PROBLEMS WITH p-LAPLACIAN OPERATOR AT RESONANCE

In this article, we consider the multi-point boundary-value problem for nonlinear fractional differential equations with p-Laplacian operator: D 0+ φp(D α 0+ u(t)) = f(t, u(t), Dα−2 0+ u(t), Dα−1 0+ u(t), D 0+ u(t)), t ∈ (0, 1), u(0) = u′(0) = D 0+ u(0) = 0, Dα−1 0+ u(1) = m X i=1 σiD α−1 0+ u(ηi), where 2 < α ≤ 3, 0 < β ≤ 1, 3 < α+β ≤ 4, Pm i=1 σi = 1, D α 0+ is the standard Riemann-Liouville ...

Solvability of Second-order Boundary-value Problems at Resonance Involving Integral Conditions

This article concerns the second-order differential equation with integral boundary conditions x′′(t) = f(t, x(t), x′(t)), t ∈ (0, 1), x(0) = Z 1 0 x(s)dα(s), x(1) = Z 1 0 x(s)dβ(s). Under the resonance conditions, we construct a projector and then applying coincidence degree theory to establish the existence of solutions.

Solvability of boundary value problems for fractional order elastic beam equations

*Correspondence: [email protected] Department of Mathematics, Guangdong University of Finance and Economics, Guangzhou, 510320, P.R. China Abstract In this article, the existence results for solutions of a boundary value problem for nonlinear singular fractional order elastic beam equations are established. The analysis relies on the well-known Schauder’s fixed point theorem. MSC: 92D25; 34A37;...