Positive Solutions of Three-Point Nonlinear Second Order Boundary Value Problem

By Youssef N. Raffoul. 2002

59 citations recorded by the source corpus.

In this paper we apply a cone theoretic xed point theorem and obtain conditions for the existence of positive solutions to the three-point nonlinear second order boundary value problem u 00 (t) + a (t)f(u(t)) = 0; t 2 (0; 1) u(0) = 0; u ( ) = u(1); where 0 < < 1 and 0 < < 1 : AMS Subject Classications: 34B20.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d9793161bf27e46425f44176d1ad5747980e4d90

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Sotiris K. Ntouyas
2. Man Kam Kwong
3. J. Henderson
4. I. Purnaras
5. Xian Xu
6. E. Kaufmann
7. Mouffak Benchohra
8. Bashir Ahmad

In Mathematical Physics

1. Sotiris K. Ntouyas
2. Xian Xu
3. I. Purnaras
4. Man Kam Kwong
5. E. Kaufmann
6. J. Henderson

In Numerical Analysis

1. Sotiris K. Ntouyas
2. Xian Xu
3. I. Purnaras
4. Man Kam Kwong
5. E. Kaufmann
6. J. Henderson
7. Mouffak Benchohra
8. Bashir Ahmad

Citations in the corpus

• Positive solutions for systems of generalized three-point nonlinear boundary value problems (2008, background): “The existence of positive solutions for three-point boundary value problems has been studied extensively in recent years.”
• Multiple sign-changing solutions for some m-point boundary-value problems. (2004, background): “Recently, there is much attention focused on the existence of nontrivial or positive solutions of the nonlinear multi-point boundary-value problems(see [3, 4, 5, 7, 9, 10, 12, 14, 15, 16, 17] and the references therein).”
• Positive Solutions for Systems of nth Order Three-point Nonlocal Boundary Value Problems (2007, unknown): “AMS (MOS) Subject Classifications: 34B18, 34A34”
• Positive solutions for systems of m‐point nonlinear boundary value problems (2008, background): “While many of these referenced papers have been devoted to scalar problems, there is much emerging interest in boundary value problems for systems of differential equations [10, 11, 18, 22, 26, 28], and a good deal of research has also involved positive solutions for multipoint nonlinear eigenvalue ”
• The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE (2006, methodology): “AMS Subject Classification: 34B10, 34B15, 34B18 Keywords: shooting method, multiple solutions, multipoint boundary value problem, secondorder ordinary differential equation”
• POSITIVE SOLUTIONS OF A THREE-POINT BOUNDARY-VALUE PROBLEM ON A TIME SCALE (2003, background): “5), which are also found in [2] and [19], will play critical roles in the proofs of our main theorems.”