## Abstract and Applied Analysis

### Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line

Yuji Liu

#### Abstract

This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian on the whole line. By constructing a suitable Banach space and a operator equation, sufficient conditions to guarantee the existence of at least three positive solutions of the BVPs are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term $[\rho (t)\mathrm{\Phi }(x’(t))]’$ involved with the function ρ, which makes the solutions un-concave.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 352159, 23 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475836

Digital Object Identifier
doi:10.1155/2012/352159

Mathematical Reviews number (MathSciNet)
MR2975303

Zentralblatt MATH identifier
1277.34026

#### Citation

Liu, Yuji. Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line. Abstr. Appl. Anal. 2012 (2012), Article ID 352159, 23 pages. doi:10.1155/2012/352159. https://projecteuclid.org/euclid.aaa/1364475836

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