Boundary Value Problems on Time Scales

Boundary Value Problems on Time Scales

Authors: Alberto Cabada and Victoria Otero-Espinar

Citation: Advances in Difference Equations 2009 2009:262719

Content type: Editorial Published on: 28 December 2009
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Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales

By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existenc...

Authors: Meiqiang Feng, Xuemei Zhang, Xianggui Li and Weigao Ge

Citation: Advances in Difference Equations 2009 2009:737461

Content type: Research Article Published on: 13 October 2009
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Some Basic Difference Equations of Schrödinger Boundary Value Problems

We consider special basic difference equations which are related to discretizations of Schrödinger equations on time scales with special symmetry properties, namely, so-called basic discrete grids. These grids...

Authors: Andreas Ruffing, Maria Meiler and Andrea Bruder

Citation: Advances in Difference Equations 2009 2009:569803

Content type: Research Article Published on: 11 October 2009
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Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales

We employ Kranoselskii's fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation

Authors: Tongxing Li, Zhenlai Han, Shurong Sun and Dianwu Yang

Citation: Advances in Difference Equations 2009 2009:562329

Content type: Research Article Published on: 11 October 2009
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Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales

We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -...

Authors: S. Gulsan Topal, O. Batit Ozen and Erbil Cetin

Citation: Advances in Difference Equations 2009 2009:123565

Content type: Research Article Published on: 19 August 2009
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Antiperiodic Boundary Value Problem for Second-Order Impulsive Differential Equations on Time Scales

We prove the existence results for second-order impulsive differential equations on time scales with antiperiodic boundary value conditions in the presence of classical fixed point theorems.

Authors: Yepeng Xing, Qiong Wang and De Chen

Citation: Advances in Difference Equations 2009 2009:567329

Content type: Research Article Published on: 3 August 2009
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Existence Results for Higher-Order Boundary Value Problems on Time Scales

By using the fixed-point index theorem, we consider the existence of positive solutions for the following nonlinear higher-order four-point singular boundary value problem on time scales ...

Authors: Jian Liu and Yanbin Sang

Citation: Advances in Difference Equations 2009 2009:209707

Content type: Research Article Published on: 29 July 2009
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Existence of Weak Solutions for Second-Order Boundary Value Problem of Impulsive Dynamic Equations on Time Scales

We study the existence of weak solutions for second-order boundary value problem of impulsive dynamic equations on time scales by employing critical point theory.

Authors: Hongbo Duan and Hui Fang

Citation: Advances in Difference Equations 2009 2009:907368

Content type: Research Article Published on: 20 July 2009
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Multiple Positive Solutions for a Class of -Point Boundary Value Problems on Time Scales

By constructing an available integral operator and combining Krasnosel'skii-Zabreiko fixed point theorem with properties of Green's function, this paper shows the existence of multiple positive solutions for a...

Authors: Meiqiang Feng, Xuemei Zhang and Weigao Ge

Citation: Advances in Difference Equations 2009 2009:219251

Content type: Research Article Published on: 19 July 2009
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Bounds for Certain New Integral Inequalities on Time Scales

Our aim in this paper is to investigate some new integral inequalities on time scales, which provide explicit bounds on unknown functions. Our results unify and extend some integral inequalities and their corr...

Authors: Wei Nian Li

Citation: Advances in Difference Equations 2009 2009:484185

Content type: Research Article Published on: 14 July 2009
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The Existence of Positive Solutions for Third-Order -Laplacian -Point Boundary Value Problems with Sign Changing Nonlinearity on Time Scales

We study the following third-order -Laplacian -point boundar...

Authors: Fuyi Xu and Zhaowei Meng

Citation: Advances in Difference Equations 2009 2009:169321

Content type: Research Article Published on: 5 July 2009
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Oscillation for Second-Order Nonlinear Delay Dynamic Equations on Time Scales

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations

Authors: Zhenlai Han, Tongxing Li, Shurong Sun and Chenghui Zhang

Citation: Advances in Difference Equations 2009 2009:756171

Content type: Research Article Published on: 29 June 2009
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Impulsive Periodic Boundary Value Problems for Dynamic Equations on Time Scale

Let T be a periodic time scale with period such that , and

Authors: Eric R. Kaufmann

Citation: Advances in Difference Equations 2009 2009:603271

Content type: Research Article Published on: 29 June 2009
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Multiple Positive Solutions for Nonlinear First-Order Impulsive Dynamic Equations on Time Scales with Parameter

By using the Leggett-Williams fixed point theorem, the existence of three positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales w...

Authors: Da-Bin Wang and Wen Guan

Citation: Advances in Difference Equations 2009 2009:830247

Content type: Research Article Published on: 22 June 2009
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Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales

This paper studies Sturm-Picone comparison theorem of second-order linear equations on time scales. We first establish Picone identity on time scales and obtain our main result by using it. Also, our result un...

Authors: Chao Zhang and Shurong Sun

Citation: Advances in Difference Equations 2009 2009:496135

Content type: Research Article Published on: 16 June 2009
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Existence of Positive Solutions in Generalized Boundary Value Problem for -Laplacian Dynamic Equations on Time Scales

We analytically establish the conditions for the existence of at least two or three positive solutions in the generalized -point boundar...

Authors: Wenyong Zhong and Wei Lin

Citation: Advances in Difference Equations 2009 2009:848191

Content type: Research Article Published on: 14 June 2009
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Existence and Uniqueness of Positive Solution for Singular BVPs on Time Scales

This paper is devoted to derive some sufficient conditions for the existence and uniqueness of positive solutions to a singular second-order dynamic equation with Dirichlet boundary conditions.

Authors: Ana Gómez González and Victoria Otero-Espinar

Citation: Advances in Difference Equations 2009 2009:728484

Content type: Research Article Published on: 11 June 2009
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Existence of Positive Solutions for Multipoint Boundary Value Problem with -Laplacian on Time Scales

We consider the existence of positive solutions for a class of second-order multi-point boundary value problem with -Laplacian on time scales. B...

Authors: Meng Zhang, Shurong Sun and Zhenlai Han

Citation: Advances in Difference Equations 2009 2009:312058

Content type: Research Article Published on: 9 June 2009
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Positive Solution to a Singular -Laplacian BVP with Sign-Changing Nonlinearity Involving Derivative on Time Scales

Let be a time scale such that . By using a monotone iterati...

Authors: You-Hui Su, Subei Li and Can-Yun Huang

Citation: Advances in Difference Equations 2009 2009:623932

Content type: Research Article Published on: 13 April 2009
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Positive Solutions for Boundary Value Problems of Second-Order Functional Dynamic Equations on Time Scales

Criteria are established for existence of least one or three positive solutions for boundary value problems of second-order functional dynamic equations on time scales. By this purpose, we use a fixed-point in...

Authors: IlkayYaslan Karaca

Citation: Advances in Difference Equations 2009 2009:829735

Content type: Research Article Published on: 16 March 2009
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