Research Article Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems
نویسندگان
چکیده
The second-order differential and difference boundary value problems arise in many branches of both applied and basic mathematics and have been extensively studied in the literature. We refer the reader to [1–4] for some recent results for second-order nonlinear two-point boundary value problems. The main tools used in the above works are fixed-point theorems. Avery and Peterson [1] generalize the fixed-point theorem of Leggett-Williams by using theory of fixed-point index and Dugundji extension theorem. Recently, Bai et al. [5] have applied this theorem to prove the existence of three positive solutions for the secondorder differential equation x′′(t) + q(t) f (t,x(t),x′(t))= 0, 0 < t < 1. In this paper, the aim of this work is to establish the existence of three positive solutions for the second-order difference equation
منابع مشابه
Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations
This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...
متن کاملExistence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales
In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.
متن کاملTriple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian
In this paper, we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian dynamic equation on time scales. We prove the existence at least three positive solutions of the boundary value problem by using the Avery and Peterson fixed point theorem. The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly. Our results ...
متن کاملPositive solutions of $n$th-order $m$-point boundary value problems
In this paper, by using four functionals fixed point theorem, we obtain sufficient conditions for the existence of at least one positive solution of an $n$th-order $m$-point boundary value problem. As an application, we give an example to demonstrate our main result.
متن کاملExistence of positive solutions for fourth-order boundary value problems with three- point boundary conditions
In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007