scholarly journals Positive Solutions of a Nonlinear Fourth-Order Dynamic Eigenvalue Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Hua Luo ◽  
Chenghua Gao
Keyword(s):  
Fixed Point ◽  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Solution Method ◽  
Lower Solution ◽  
Existence Results ◽  
Fourth Order Eigenvalue Problem ◽  
Existence And Nonexistence ◽  
Lower Solution Method

LetTbe a time scale anda,b∈T,a<ρ2(b). We study the nonlinear fourth-order eigenvalue problem onT,uΔ4(t)=λh(t)f(u(t),uΔ2(t)),t∈[a,ρ2(b)]T,u(a)=uΔ(σ(b))=uΔ2(a)=uΔ3(ρ(b))=0and obtain the existence and nonexistence of positive solutions when0<λ≤λ*andλ>λ*, respectively, for someλ*. The main tools to prove the existence results are the Schauder fixed point theorem and the upper and lower solution method.

Existence and Multiplicity of Positive Solutions for Singular Semipositone p-Laplacian Equations

2006 ◽  
Vol 58 (3) ◽  
pp. 449-475 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Daomin Cao ◽  
Haishen Lü ◽  
Donal O'Regan
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Solution Method ◽  
Degree Theory ◽  
Lower Solution ◽  
Existence And Multiplicity ◽  
Lower Solution Method ◽  
Multiplicity Of Positive Solutions ◽  
Image Position ◽  
Laplacian Equations

AbstractPositive solutions are obtained for the boundary value problemHere f (t, u) ≥ –M, (M is a positive constant) for (t, u) ∈ [0, 1]×(0, ∞). We will show the existence of two positive solutions by using degree theory together with the upper–lower solution method.

scholarly journals Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongping Sun ◽  
Qian Sun ◽  
Xiaoping Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Existence Results ◽  
Functional Type ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Cone Expansion And Compression

This paper is concerned with the existence and nonexistence of positive solutions for a nonlinear higher-order three-point boundary value problem. The existence results are obtained by applying a fixed point theorem of cone expansion and compression of functional type due to Avery, Henderson, and O’Regan.

scholarly journals Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Jingjing Cai ◽  
Guilong Liu
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence And Nonexistence

Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces.

scholarly journals Upper and Lower Solution Method for Fourth-Order Four-Point Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Ilkay Yaslan Karaca
Keyword(s):  
Boundary Value Problem ◽  
Time Scales ◽  
Fourth Order ◽  
Solution Method ◽  
Boundary Value ◽  
Lower Solution ◽  
Point Boundary ◽  
Upper And Lower Solution ◽  
Lower Solution Method ◽  
Order Four

We consider a fourth-order four-point boundary value problem for dynamic equations on time scales. By the upper and lower solution method, some results on the existence of solutions of the fourth-order four-point boundary value problem on time scales are obtained. An example is also included to illustrate our results.

scholarly journals Existence of Positive Solutions to Singular -Laplacian General Dirichlet Boundary Value Problems with Sign Changing Nonlinearity

2009 ◽  
Vol 2009 ◽  
pp. 1-21 ◽  
Author(s):  
Qiying Wei ◽  
You-Hui Su ◽  
Subei Li ◽  
Xing-Xue Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Solution Method ◽  
Dirichlet Boundary ◽  
Lower Solution ◽  
Existence Of Positive Solutions ◽  
Lower Solution Method ◽  
Existence Criteria ◽  
General Time

By using the well-known Schauder fixed point theorem and upper and lower solution method, we present some existence criteria for positive solution of an -point singular -Laplacian dynamic equation on time scales with the sign changing nonlinearity. These results are new even for the corresponding differential () and difference equations (), as well as in general time scales setting. As an application, an example is given to illustrate the results.

Sign in / Sign up

Export Citation Format

Share Document