Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems

Lin, Longfei; Liu, Yansheng; Deng-feng, Zhao

doi:10.3390/sym12121989

Cited by 4 publications

(1 citation statement)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For instance, the deformation of an elastic beam under an external force h supported at both ends is described by the linear boundary value problem x (4) (t) = h(t), t ∈ (0, 1), x(0) = x(1) = x ′′ (0) = x ′′ (1) = 0, where vanishing moments at the ends of the attached beam motivate the boundary conditions (see [9] for more details). The existence of solutions for nonlinear fourth-order BVPs has gained much interest in the last years (see, e.g., [2,3,4,6,10,11,12,13,15,17]). Boundary value problems with integral boundary conditions constitute a very interesting and important class of problems.…”

Section: Introductionmentioning

confidence: 99%

Multiple Nonnegative Solutions for a Class of Fourth-Order BVPs Via a New Topological Approach

BENSLİMANE

Georgiev

Mebarki

2022

Advances in the Theory of Nonlinear Analysis and Its Application

View full text Add to dashboard Cite

In this paper, we propose extensions of Leray-Schauder boundary condition for a sum of two operators T + S in the case when T is an expansive operator and I − S is a completely continuous operator. As their applications, we investigate a class of fourth-order nonlinear boundary value problems with integral boundary conditions. We give conditions for the parameters of the considered boundary value problem that ensure existence of at least two non trivial bounded nonnegative classical solutions of the considered boundary value problem. The results in the paper are provided with a suitable example.

show abstract

Section: Introductionmentioning

confidence: 99%

Multiple Nonnegative Solutions for a Class of Fourth-Order BVPs Via a New Topological Approach

BENSLİMANE

Georgiev

Mebarki

2022

Advances in the Theory of Nonlinear Analysis and Its Application

View full text Add to dashboard Cite

show abstract

Existence of solutions of nonlinear systems subject to arbitrary linear non-local boundary conditions

Cabada,

López-Somoza,

Yousfi

2023

J. Fixed Point Theory Appl.

View full text Add to dashboard Cite

In this paper, we obtain an explicit expression for the Green’s function of a certain type of systems of differential equations subject to non-local linear boundary conditions. In such boundary conditions, the dependence on certain parameters is considered. The idea of the study is to transform the given system into another first-order differential linear system together with the two-point boundary value conditions. To obtain the explicit expression of the Green’s function of the considered linear system with non-local boundary conditions, it is assumed that the Green’s function of the homogeneous problem, that is, when all the parameters involved in the non-local boundary conditions take the value zero, exists and is unique. In such a case, the homogeneous problem has a unique solution that is characterized by the corresponding Green’s function g. The expression of the Green’s function of the given system is obtained as the sum of the function g and a part that depends on the parameters involved in the boundary conditions and the expression of function g. The novelty of our work is that in the system to be studied, the unknown functions do not appear separated neither in the equations nor in the boundary conditions. The existence of solutions of nonlinear systems with linear non-local boundary conditions is also studied. We illustrate the obtained results in this paper with examples.

show abstract

On the Existence of Non-Spurious Solutions to Second Order Dirichlet Problem

et al. 2021

View full text Add to dashboard Cite

show abstract

Multiple Solutions for a Class of Nonlinear Fourth-Order Boundary Value Problems

Cited by 4 publications

References 31 publications

Multiple Nonnegative Solutions for a Class of Fourth-Order BVPs Via a New Topological Approach

Multiple Nonnegative Solutions for a Class of Fourth-Order BVPs Via a New Topological Approach

Existence of solutions of nonlinear systems subject to arbitrary linear non-local boundary conditions

On the Existence of Non-Spurious Solutions to Second Order Dirichlet Problem

Contact Info

Product

Resources

About