Nonzero Solutions for Nonlinear Systems of Fourth-Order Boundary Value Problems

This study is devoted to the investigation of nonlinear systems of fourth-order boundary value problems. Namely, using some techniques from matrix analysis and ordinary differential equations, a Lyapunov-type inequality providing a necessary condition for the existence of nonzero solutions is obtained. Next, an estimate involving generalized eigenvalues is derived as an application of our main result.

Lyapunov-type inequality for higher order left and right fractional p-Laplacian problems

In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, we apply the Schaefer’s fixed point theorem. Furthermore, we present the Lyapunov inequality for the corresponding problem.

Lyapunov-type inequality for a Riemann-Liouville type fractional boundary value problem with anti-periodic boundary conditions

In this article, we establish a Lyapunov-type inequality for a two-point Riemann-Liouville type fractional boundary value problem associated with well-posed anti-periodic boundary conditions. As an application, we estimate a lower bound for the eigenvalue of the corresponding fractional eigenvalue problem.

Lyapunov Type Inequality for an Anti-Periodic Conformable Boundary Value Problem

In this article, we present a Lyapunov-type inequality for a conformable boundary value problem associated with anti-periodic boundary conditions. To demonstrate the applicability of established result, we obtain a lower bound on the eigenvalue of the corresponding eigenvalue problem.

Analysis of some Katugampola fractional differential equations with fractional boundary conditions

<abstract><p>In this work, some class of the fractional differential equations under fractional boundary conditions with the Katugampola derivative is considered. By proving the Lyapunov-type inequality, there are deduced the conditions for existence, and non-existence of the solutions to the considered boundary problem. Moreover, we present some examples to demonstrate the effectiveness and applications of the new results.</p></abstract>

A New Proof for Lyapunov-Type Inequality on the Fractional Boundary Value Problem

In this article, some new Lyapunov-type inequalities for a class of fractional boundary value problems are established by use of the nonsymmetry property of Green’s function corresponding to appropriate boundary conditions.

Existence and uniqueness of mild solutions for a fractional differential equation under Sturm-Liouville boundary conditions when the data function is of Lipschitzian type

In this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of Lipschitzian type. Moreover, we present an application of our result to the eigenvalues problem and its connection with a Lyapunov-type inequality.