scholarly journals Sufficient condition for existence of solutions for higher-order resonance boundary value problem with one-dimensional p-Laplacian

2007 ◽  
pp. 1-11 ◽  
Author(s):  
Liu Yang ◽  
Chunfang Shen ◽  
Xiping Liu
Keyword(s):  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Sufficient Condition ◽  
One Dimensional ◽  
Order Resonance

scholarly journals Solutions of a multi-point boundary value problem for higher-order differential equations at resonance (III)

2005 ◽  
Vol 36 (2) ◽  
pp. 119-130 ◽  
Author(s):  
Yuji Liu ◽  
Weigao Ge
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
At Resonance ◽  
Higher Order Differential Equations

In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equations$ x^{(n)}(t)=f(t,x(t),x'(t),\cdots,x^{(n-1)}(t))+e(t),\;\;0

scholarly journals Solvability of a Class of Higher-Order Fractional Two-Point Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Xiangshan Kong ◽  
Haitao Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Green's Function ◽  
Point Theorem ◽  
Caputo Derivative ◽  
Boundary Value ◽  
Higher Order ◽  
Sufficient Condition ◽  
Point Boundary

This paper investigates the solvability of a class of higher-order fractional two-point boundary value problem (BVP), and presents several new results. First, Green’s function of the considered BVP is obtained by using the property of Caputo derivative. Second, based on Schaefer’s fixed point theorem, the solvability of the considered BVP is studied, and a sufficient condition is presented for the existence of at least one solution. Finally, an illustrative example is given to support the obtained new results.

Existence of solutions to three-point boundary value problem for one-dimensional p-Laplacian

2008 ◽  
Vol 30 (1-2) ◽  
pp. 447-457
Author(s):  
Huixing Zhang ◽  
Wenbin Liu ◽  
Jianjun Zhang ◽  
Taiyong Chen
Keyword(s):  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
One Dimensional

System of nonlocal resonant boundary value problems involving p-Laplacian

2018 ◽  
Vol 68 (4) ◽  
pp. 837-844
Author(s):  
Katarzyna Szymańska-Dębowska
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Bounded Variation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Function Of Bounded Variation ◽  
One Dimensional ◽  
The One

Abstract Our aim is to study the existence of solutions for the following system of nonlocal resonant boundary value problem $$\begin{array}{} \displaystyle (\varphi (x'))' =f(t,x,x'),\quad x'(0)=0, \quad x(1)=\int\limits_{0 }^{1}x(s){\rm d} g(s), \end{array}$$ where the function ϕ : ℝn → ℝn is given by ϕ (s) = (φp1(s1), …, φpn(sn)), s ∈ ℝn, pi > 1 and φpi : ℝ → ℝ is the one dimensional pi -Laplacian, i = 1,…,n, f : [0,1] × ℝn × ℝn → ℝn is continuous and g : [0,1] → ℝn is a function of bounded variation. The proof of the main result is depend upon the coincidence degree theory.

scholarly journals Necessary and Sufficient Condition for the Existence of Solutions to a Discrete Second-Order Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Chenghua Gao
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Sufficient Condition ◽  
First Eigenvalue ◽  
Necessary And Sufficient Condition ◽  
The First Eigenvalue ◽  
Necessary And Sufficient

This paper is concerned with the existence of solutions for the discrete second-order boundary value problemΔ2u(t-1)+λ1u(t)+g(Δu(t))=f(t),t∈{1,2,…,T},u(0)=u(T+1)=0, whereT>1is an integer,f:{1,…,T}→R,g:R→Ris bounded and continuous, andλ1is the first eigenvalue of the eigenvalue problemΔ2u(t-1)+λu(t)=0,t∈T,u(0)=u(T+1)=0.

scholarly journals On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Rossitza Semerdjieva
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Sufficient Condition ◽  
Free Boundary Value Problem ◽  
Necessary And Sufficient Condition ◽  
One Dimensional ◽  
Necessary And Sufficient ◽  
Infinite Differentiability ◽  
Differential Condition

AbstractWe consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on Cm-smoothness of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.

Existence of Solutions for a Higher Order Multi-Point Boundary Value Problem

2008 ◽  
Vol 53 (1-2) ◽  
pp. 77-101 ◽  
Author(s):  
John R. Graef ◽  
Lingju Kong ◽  
Bo Yang
Keyword(s):  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary

scholarly journals EXISTENCE OF SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR p-LAPLACIAN BOUNDARY VALUE PROBLEM

2013 ◽  
Vol 11 (02) ◽  
pp. 1350004 ◽  
Author(s):  
WEI-CHENG LIAN ◽  
WEI-CHUAN WANG ◽  
YAN-HSIOU CHENG
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
One Dimensional ◽  
Laplacian Equation ◽  
Separated Boundary Conditions ◽  
Sign Changing Solutions ◽  
Nodal Properties

We study the nonlinear one-dimensional p-Laplacian equation [Formula: see text] where p > 1, y(p-1) = |y|p-1 sgn y = |y|p-2y, with linear separated boundary conditions. We give sufficient conditions for the existence of solutions with prescribed nodal properties concerning the behavior of f(s)/s(p-1) when s is at infinity and zero, respectively. These results are more general and complementary than previous known ones for the case when p = 2 and q is nonnegative.

Existence of solutions for a higher order fractional boundary value problem posed on the half-line

2019 ◽  
Vol 12 (01) ◽  
pp. 1950008
Author(s):  
A. Boucenna ◽  
T. Moussaoui
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Monotone Operators ◽  
Higher Order ◽  
Half Line ◽  
Fractional Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Continuous Embedding

The aim of this paper is to study the existence and uniqueness of solutions for a boundary value problem associated with a fractional nonlinear differential equation with higher order posed on the half-line. An appropriate continuous embedding for suitable Banach spaces are proved and the Minty–Browder theorem for monotone operators is used in the proof of existence of solutions for a boundary value problem of fractional order posed on the half-line.

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