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Positive Solutions for a Class of Nonresonant m-Point Boundary Value Problems
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M. Feng
Published/Copyright:
June 9, 2010
Abstract
This paper concerns the existence and multiplicity of positive solutions for a class of nonresonant m-point boundary-value problem of second-order differential equations Lx = λw(t)ƒ(t, x), 0 < t < 1. The interesting points are that Lx ≔ –x″ + ρqx and w is Lp-integrable for some 1 ≤ p ≤ +∞. The arguments are based upon fixed point theorems in a cone and Hölder's inequality. The nonexistence of positive solution is also studied. In addition, some examples are included to demonstrate the main results.
Key words and phrases.: Positive solution; fixed point theorem; existence; complete continuity; m-point boundary value problems
Received: 2006-08-28
Revised: 2008-01-25
Published Online: 2010-06-09
Published in Print: 2008-June
© Heldermann Verlag
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Keywords for this article
Positive solution;
fixed point theorem;
existence;
complete continuity;
m-point boundary value problems
Articles in the same Issue
- Finite Partitions of Topological Groups into Congruent Thick Subsets
- Derivatives of Markov Kernels and Their Jordan Decomposition
- Sufficiency and Duality in Control Problems with Generalized Invexity
- Koebe Domains for the Classes of Functions with Ranges Included in Given Sets
- Upper and Lower Solutions Method for Fourth-Order Periodic Boundary Value Problems
- Efficiency and Duality for Generalized Convex Multiobjective Programming
- General Mixed Vector F-Implicit Complementarity Problems in Banach Spaces
- Modelling and Products of Singularities in Colombeau's Algebra
- Set Differential Equations in Fréchet Spaces
- Positive Solutions for a Class of Nonresonant m-Point Boundary Value Problems
- Second Order Duality in Multiobjective Programming
