# The existence of three positive solutions for some nonlinear boundary value problems on the half-line

The existence of three positive solutions for some nonlinear boundary value problems on the... In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we consider the existence of triple positive solutions for some nonlinear m-point boundary value problems on the half-line $$(\varphi(u^\prime))^\prime + a(t)f(t, u(t)) = 0, \quad 0 < t <+\infty,$$ $$u(0) = \sum_{i=1}^{m-2} \alpha_iu(\xi_i), \quad u^\prime(\infty) = 0,$$ where $${\varphi:}R {\rightarrow}R$$ is the increasing homeomorphism and positive homomorphism and $$\varphi(0) =0$$ . We show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term by using the five functionals fixed-point theorem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# The existence of three positive solutions for some nonlinear boundary value problems on the half-line

, Volume 13 (2) – Jul 5, 2008
15 pages

/lp/springer_journal/the-existence-of-three-positive-solutions-for-some-nonlinear-boundary-9duASubOc0
Publisher
Birkhäuser-Verlag
Copyright © 2008 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2213-z
Publisher site
See Article on Publisher Site

### Abstract

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p > 1, we consider the existence of triple positive solutions for some nonlinear m-point boundary value problems on the half-line $$(\varphi(u^\prime))^\prime + a(t)f(t, u(t)) = 0, \quad 0 < t <+\infty,$$ $$u(0) = \sum_{i=1}^{m-2} \alpha_iu(\xi_i), \quad u^\prime(\infty) = 0,$$ where $${\varphi:}R {\rightarrow}R$$ is the increasing homeomorphism and positive homomorphism and $$\varphi(0) =0$$ . We show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term by using the five functionals fixed-point theorem.

### Journal

PositivitySpringer Journals

Published: Jul 5, 2008

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