A nonlinear boundary value problem for fourth-order elastic beam equations

Song, Yuanping

doi:10.1186/s13661-014-0191-6

Cited by 13 publications

(9 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…according to the displacement registered in the right end. Various methods were used to deal with the existence of solutions of the boundary value problem (BVP) (1.1)-(1.2), for example variational methods in [9,78], iterative methods in [1,62,64] and topological methods in [36].…”

Section: Introductionmentioning

confidence: 99%

Solutions of perturbed Hammerstein integral equations with applications

Cianciaruso

Infante

Pietramala

2017

Nonlinear Analysis: Real World Applications

View full text Add to dashboard Cite

Abstract. By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical results, we study some problems that occur in applied mathematics, namely models of chemical reactors, beams and thermostats. We also apply our theory in order to prove the existence of nontrivial radial solutions of systems of elliptic boundary value problems subject to nonlocal, nonlinear boundary conditions.

show abstract

Section: Introductionmentioning

confidence: 99%

Solutions of perturbed Hammerstein integral equations with applications

Cianciaruso

Infante

Pietramala

2017

Nonlinear Analysis: Real World Applications

View full text Add to dashboard Cite

show abstract

“…In recent years, much attention has been paid to elastic beam equations. Various tools ad methods have been applied to study the existence, uniqueness and multiplicity of solutions for problem (1.1), for example topological degree theory [5][6][7][8], the monotone iteration method [9][10][11][12][13], partial order theory [14,15], and critical point theory [16,17]. We would like to mention some results of [5,6,9,14], which motivated us to consider problem (1.1).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation

Sang

Ren

2019

Bound Value Probl

View full text Add to dashboard Cite

In this paper, by studying the solutions of the abstract operator equation A(x, x) + B(x, x) + e = x on ordered Banach spaces, where A, B are two mixed monotone operators and e ∈ P with θ ≤ e ≤ h, we prove a class of boundary value problems on elastic beam equation to have a unique solution. Furthermore, we also apply our abstract result to establish the existence and uniqueness theorem of nontrivial solutions for nonlinear fractional boundary value problems. The iterative sequences to approximate unique solutions for the above two classes of problems are also obtained.

show abstract

“…Geng and Cui [23] developed a method for solving nonlinear quadratic two-point BVP with the combination of ADM and RKM. Further detail can be found in studies of fourth-order boundary value problems [23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%