Positive and maximal positive solutions of singular mixed boundary value problem

2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Ravi Agarwal ◽  
Donal O’Regan ◽  
Svatoslav Staněk
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Mixed Boundary Value Problem ◽  
Time Singularity ◽  
Strong Singularity

AbstractThe paper is concerned with existence results for positive solutions and maximal positive solutions of singular mixed boundary value problems. Nonlinearities h(t;x;y) in differential equations admit a time singularity at t=0 and/or at t=T and a strong singularity at x=0.

scholarly journals Artificial small parameter method—solving mixed boundary value problems

2005 ◽  
Vol 2005 (3) ◽  
pp. 325-340 ◽  
Author(s):  
I. V. Andrianov ◽  
J. Awrejcewicz ◽  
A. Ivankov
Keyword(s):  
Boundary Value Problem ◽  
Small Parameter ◽  
Boundary Value Problems ◽  
Computational Efficiency ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Parameter Method ◽  
Mixed Boundary Value Problem ◽  
Small Parameter Method ◽  
Novel Method

A novel method for solving mixed boundary value problem is presented. A computational efficiency of the proposed method is illustrated using a few mechanical examples.

scholarly journals POSITIVE SOLUTIONS FOR NON-RESONANT SINGULAR BOUNDARY-VALUE PROBLEMS WITH A LINEAR TERM

2007 ◽  
Vol 50 (1) ◽  
pp. 217-228 ◽  
Author(s):  
Haishen Lü ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Linear Term ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems

AbstractThis paper presents new existence results for the singular boundary-value problem\begin{gather*} -u''+p(t)u=f(t,u),\quad t\in(0,1),\\ u(0)=0=u(1). \end{gather*}In particular, our nonlinearity $f$ may be singular at $t=0,1$ and $u=0$.

scholarly journals Existence of Positive Solutions for a Functional Fractional Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Chuanzhi Bai
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Functional Differential

We study the existence of positive solutions for a boundary value problem of fractional-order functional differential equations. Several new existence results are obtained.

scholarly journals Positive Solutions for a Class of Discrete Mixed Boundary Value Problems with the p,q-Laplacian Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Cuiping Li ◽  
Zhan Zhou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Critical Points ◽  
Existence Of Solutions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Mixed Boundary Value Problems

In this paper, we consider the existence of solutions for the discrete mixed boundary value problems involving p,q-Laplacian operator. By using critical points theory, we obtain the existence of at least two positive solutions for the boundary value problem under appropriate assumptions on the nonlinearity.

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