Abstract
Using a fixed point theorem of general -concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions for two classes of nonlinear perturbed Neumann boundary value problems for second-order differential equations. The theorems for Neumann boundary value problems obtained are very general.
Highlights
Introduction and PreliminariesWe are interested in the existence and uniqueness of positive solutions for the following nonlinear perturbed Neumann boundary value problems NBVPs :
Introduction and PreliminariesIn this paper, we are interested in the existence and uniqueness of positive solutions for the following nonlinear perturbed Neumann boundary value problems NBVPs : ⎧⎨±u t m2u t f t, u t g t, 0 < t < 1, P± ⎩u 0 u 1 0, 1.1 where m is a positive constant, f : 0, 1 × 0, ∞ → 0, ∞ and g : 0, 1 → 0, ∞ are continuous.It is well known that Neumann boundary value problem for the ordinary differential equations and elliptic equations is an important kind of boundary value problems
We are interested in the existence and uniqueness of positive solutions for the following nonlinear perturbed Neumann boundary value problems NBVPs :
Summary
We are interested in the existence and uniqueness of positive solutions for the following nonlinear perturbed Neumann boundary value problems NBVPs :. ⎨±u t m2u t f t, u t g t , 0 < t < 1, P± ⎩u 0 u 1 0, 1.1 where m is a positive constant, f : 0, 1 × 0, ∞ → 0, ∞ and g : 0, 1 → 0, ∞ are continuous. It is well known that Neumann boundary value problem for the ordinary differential equations and elliptic equations is an important kind of boundary value problems. During the last two decades, Neumann boundary value problems have deserved the attention of many researchers 1–10. By using-fixed point theorems in cone, in 1, 5, 7–9 , the authors discussed the existence of positive solutions for ordinary differential equation Neumann boundary value problems
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