Positive solutions for nonlocal fourth-order boundary value problems with all order derivatives

Guo, Yongfeng; Yang, Fei; Liang, Yongchun

doi:10.1186/1687-2770-2012-29

Cited by 9 publications

(7 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The nonlinearity f in [6,17] is not affected by the slope and bending moment, and the authors used the method of fixed point index on cone. We also refer to some other articles, for instance, [2,5,7,9,14,19].…”

Section: Introductionmentioning

confidence: 99%

Inequalities of Green’s functions and positive solutions to nonlocal boundary value problems

2020

View full text Add to dashboard Cite

In this paper, we discuss the positive solutions of beam equations with the nonlinearities including the slope and bending moment under nonlocal boundary conditions involving Stieltjes integrals. We pose some inequality conditions on nonlinearities and the spectral radius conditions on associated linear operators. These conditions mean that the nonlinearities have superlinear or sublinear growth. The existence of positive solutions is obtained by fixed point index on cones in C 2 [0, 1], and some examples are given for beam equations subject to mixed integral and multi-point boundary conditions with sign-changing coefficients. MSC: Primary 34B18; 34B10; secondary 34B15 Keywords: Positive solution; Fixed point index; Cone; Spectral radius u(t) dB i (t) and α i [u] = 1 0 u(t) dA i (t) © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material.

show abstract

Section: Introductionmentioning

confidence: 99%

Inequalities of Green’s functions and positive solutions to nonlocal boundary value problems

2020

View full text Add to dashboard Cite

show abstract

“…Their methods are respectively based on fixed point index theory on cones and global bifurcation techniques. Bai [5] and Guo et al [6] explored the existence of positive solutions respectively for the nonlocal fourth-order problems where p, q ∈ L[0, 1] are nonnegative. Li [7] discussed the existence of positive solutions for a local fully nonlinear problem…”

Section: Introductionmentioning

confidence: 99%

Positive solutions of beam equations under nonlocal boundary value conditions

2019

View full text Add to dashboard Cite

In this article, we study the fourth-order problem with the first and second derivatives in nonlinearity under nonlocal boundary value conditions2, 3). This equation describes the deflection of an elastic beam. Some inequality conditions on nonlinearity f are presented that guarantee the existence of positive solutions to the problem by the theory of fixed point index on a special cone in C 2 [0, 1]. Two examples are provided to support the main results under mixed boundary conditions involving multi-point with sign-changing coefficients and integral with sign-changing kernel. MSC: Primary 34B18; 34B10; secondary 34B15 Keywords: Positive solution; Fixed point index; Cone where β i [u] = 1 0 u(t) dB i (t) is Stieltjes integral with B i of bounded variation (i = 1, 2, 3). This equation describes the deflection of an elastic beam. Alves et al. [1] established the existence of positive solutions for the beam equationu (4) (t) = f t, u(t), u (t) under boundary conditions u(0) = u (0) = 0, u (1) = g u(1) , u (1) = 0 or u (1) = 0,

show abstract

“…In [2], Guo, Yang and Liang showed the existence of positive solutions to (1.1)-(1.2) by defining two positive continuous convex functionals. Based on a fixed point theorem due to Guo and Ge [3] and the nonlocal fourth-order BVPs Green function, some criteria for the existence of positive solutions were obtained; see [2] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Positive solutions for some nonlocal elastic beam equation boundary value problems with fully nonlinear term

2018

J. Nonlinear Funct. Anal.

View full text Add to dashboard Cite

show abstract

Positive solutions for nonlocal fourth-order boundary value problems with all order derivatives

Cited by 9 publications

References 13 publications

Inequalities of Green’s functions and positive solutions to nonlocal boundary value problems

Inequalities of Green’s functions and positive solutions to nonlocal boundary value problems

Positive solutions of beam equations under nonlocal boundary value conditions

Positive solutions for some nonlocal elastic beam equation boundary value problems with fully nonlinear term

Contact Info

Product

Resources

About