Positive solutions for nonlinear discrete second-order boundary value problems with parameter dependence

In this paper, we consider the nonlinear discrete boundary value problem

     

Uniqueness and parameter dependence of positive solutions to higher order boundary value problems with fractional $q$-derivatives

The authors study a class of nonlinear higher order boundary value problem with fractional $q$-erivativesand dependence on a positive parameter $\lm$.The existence, uniqueness, and dependence of positive solutions on $\lm$ are discussed.Two sequences are constructed so that they converge uniformly to the unique solution of the problems.Two examples are included in the paper. Numerical computations of the examples confirm their theoretical results.     

Uniqueness of solutions for third-order two-point boundary value problems

This paper is devoted to study the uniqueness of solutions for the third-order boundary value problems. Differential inequalities and fixed point theorem are used. In particular, nonlinearity term is a L ^p -Carathédory function, p≥1.     

Uniqueness of positive solutions for quasilinear boundary value problems

Sufficient conditions for the uniqueness of positive solutions of boundary value problems for quasilinear differential equations of the type

(|u′|^m−2u′)′ + f(t,u,u′)=0, m 2

are established. These problems arise, for example, in the study of the m-Laplace equation in annular regions.     

Uniqueness of positive solutions for Sturm-Liouville boundary value problems

Sufficient conditions for the uniqueness of positive solutions of singular Sturm-Liouville boundary value problems

where and , are established.

     

奇异二阶Neumann边值问题的正解

考察非线性二阶边值问题-u″(t)+λu(t)=h(t)f(t,u(t))+ζ(t,u(t)),0＜t＜1,u′(0)=u′(1)=0,的正解,其中λ＞0.文中允许ζ(t,u)在t=0,t=1和u=0处奇异.利用锥上的Guo-KraLsnosel'skii不动点定理证明了n个正解的存在性,其中n是任意的正整数.     

一类二阶三点边值问题的解和多解性

利用锥拉伸与锥压缩型Krasnosel'skii不动点定理,给出了一类非线性二阶三点边值问题解和多解的存在性定理,其中允许非线性项有一个负的下界,本文的结论表明该方程可以具有n个解和正解,从而推广和改进了已有的解的存在性的结论.     

Multiple positive solutions for second-order m-point boundary value problems

In this paper, the second-order m-point boundary value problem

     

Positive solutions for some second-order four-point boundary value problems

In this paper, the second-order four-point boundary value problem

     

Nontrivial solutions of boundary value problems of second-order difference equations

We employ the critical point theory to establish the existence of nontrivial solutions for some boundary value problems of second-order difference equations.     

The existence of solutions to second-order singular boundary value problems

This article analyzes qualitative properties of solutions to two-point boundary value problems for singular ordinary differential equations. In particular, we form new approaches that ensure that all possible solutions satisfy certain a priori bounds. The methods involve differential inequalities.     

Existence and nonexistence of solutions of second-order nonlinear boundary value problems

We study the nonlinear boundary value problem consisting of the equation −y^″+q(t)y=w(t)f(y) on [a,b]$-y^{″}+q\left(t\right)y=w\left(t\right)f\left(y\right)\text{ on }[a,b]$ and a general separated homogeneous linear boundary condition. By comparing this problem with a corresponding linear Sturm–Liouville problem we obtain conditions for the existence and nonexistence of solutions of this problem. More specifically, let _λn,n=0,1,2,…${\lambda }_n,n=0,1,2,\dots$, be the n$n$-th eigenvalues of the corresponding linear Sturm–Liouville problem. Then under certain assumptions, the boundary value problem has a solution with exactly n$n$ zeros in (a,b)$(a,b)$ if _λn${\lambda }_n$ is in the interior of the range of f(y)/y,y∈(0,∞)$f\left(y\right)/y,y\in (0,\infty )$; and does not have any solution with exactly n$n$ zeros in (a,b)$(a,b)$ if _λn${\lambda }_n$ is outside of the range of f(y)/y,y∈(0,∞)$f\left(y\right)/y,y\in (0,\infty )$. These conditions become necessary and sufficient when f(y)/y$f\left(y\right)/y$ is monotone. The existences of multiple and even an infinite number of solutions are derived as consequences. We also discuss the changes of the number and the types of nontrivial solutions as the interval [a,b]$[a,b]$ shrinks, as q$q$ increases in a given direction, and as the boundary condition changes.     

Three symmetric positive solutions for second-order nonlocal boundary value problems

Using the Leggett-Williams fixed point theorem,we will obtain at least three symmetric positive solutions to the second-order nonlocal boundary value problem of the form u(t)+g(t)f(t,u(t))=0,0相似文献