Triple positive solutions of conjugate boundary value problems

Wong, Patricia J. Y.

doi:10.1016/s0898-1221(98)00190-4

Cited by 37 publications

(20 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next, for all v ∈ , by (21) and (22), respectively, we have α v ≤ β v and v ≤ t m − a / t 0 − a γ v . To show that P γ c → P γ c , let v ∈ P γ c .…”

Section: Three Symmetric Positive Solutions: the Continuous Casementioning

confidence: 98%

“…There is much current attention focused on questions of positive solutions of boundary value problems for ordinary differential equations, as well as for finite difference equations; see, to name a few, [5,6,9,11,[13][14][15][19][20][21][22][23][24]. Much of this interest is due to the applicability of certain fixed point theorems of Krasnosel'skii [17] or Leggett and Williams [18] to obtaining positive solutions or multiple positive solutions which lie in a cone.…”

mentioning

confidence: 99%

See 1 more Smart Citation

General Lidstone Problems: Multiplicity and Symmetry of Solutions

Davis

Henderson

Wong

2000

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…Next, for all v ∈ , by (21) and (22), respectively, we have α v ≤ β v and v ≤ t m − a / t 0 − a γ v . To show that P γ c → P γ c , let v ∈ P γ c .…”

Section: Three Symmetric Positive Solutions: the Continuous Casementioning

confidence: 98%

mentioning

confidence: 99%

General Lidstone Problems: Multiplicity and Symmetry of Solutions

Davis

Henderson

Wong

2000

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…The subject of (k, n − k) conjugate boundary value problems have a wide range of applications, for example in material mechanics and physical sciences, such as be used to model the deformation of elastic beams. Recently, many people paid attention to existence result of solution of (k, n − k) conjugate boundary value problems, such as [10,13,18,31,34,36,44]. If n = 4 and k = 2, then the conjugate boundary value problem reduces to the fourth order problem, because it describes the deflection of an elastic beam under a certain force.…”

Section: Application To Boundary Value Problemsmentioning

confidence: 99%

Existence and uniqueness of iterative positive solutions for singular Hammerstein integral equations

Zhang¹,

Liu²,

Wu³

2017

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

In this article, we study the existence and the uniqueness of iterative positive solutions for a class of nonlinear singular integral equations in which the nonlinear terms may be singular in both time and space variables. By using the fixed point theorem of mixed monotone operators in cones, we establish the conditions for the existence and uniqueness of positive solutions to the problem. Moreover, we derive various properties of the positive solutions to the equation and establish their dependence on the model parameter. The theorem obtained in this paper is more general and complements many previous known results including singular and nonlinear cases. Application of the results to the study of differential equations are also given in the article.

show abstract

“…For examples, in [4,6,14,16,24,25,26,35,40,48,50], the following (n, n − k) type problems were studied: In [23,27], the following more general boundary value problems were studied:…”

Section: 1mentioning

confidence: 99%

A survey and new investigation on $(n,n-k)$-type boundary value problems for higher order impulsive fractional differential equations

Liu

2017

Tbilisi Math. J.

View full text Add to dashboard Cite

A survey for studies on boundary value problems of higher order ordinary differential equations is given firstly. Secondly a simple review for studies on solvability of boundary value problems for impulsive fractional differential equations is presented. Thirdly by using a general method for converting an impulsive fractional differential equation with the Riemann-Liouville fractional derivatives to an equivalent integral equation and employing fixed point theorems in Banach space, we establish existence results of solutions for three classes of boundary value problems ((n, n − k) type BVPs) of impulsive higher order fractional differential equations. Some examples are presented to illustrate the efficiency of the results obtained and some mistakes are also corrected at the end of the paper finally. A conclusion section is given at the end of the paper.

show abstract

Triple positive solutions of conjugate boundary value problems

Cited by 37 publications

References 5 publications

General Lidstone Problems: Multiplicity and Symmetry of Solutions

General Lidstone Problems: Multiplicity and Symmetry of Solutions

Existence and uniqueness of iterative positive solutions for singular Hammerstein integral equations

A survey and new investigation on $(n,n-k)$-type boundary value problems for higher order impulsive fractional differential equations

Contact Info

Product

Resources

About