Multiple positive solutions to mixed boundary value problems for singular ordinary differential equations on the whole line
Articles
Yuji Yuji
Guangdong University of Business Studies, China
Published 2012-10-25
https://doi.org/10.15388/NA.17.4.14051
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Keywords

Second order differential equation with quasi-Laplacian on the whole line
integral type boundary value problem
positive solution
fixed point theorem

How to Cite

Yuji Y. (2012) “Multiple positive solutions to mixed boundary value problems for singular ordinary differential equations on the whole line”, Nonlinear Analysis: Modelling and Control, 17(4), pp. 460-480. doi: 10.15388/NA.17.4.14051.

Abstract

This paper is concerned with the mixed boundary value problem of the second order singular ordinary differential equation
[Φ(ρ(t)x'(t))]' + f(t, x(t), x'(t)) = 0,   t ∈ R,
limt→−∞x(t) = −∞+∞g(s, x(s), x'(s)) ds,
limt→+∞ρ(t)x'(t) = −∞+∞h(s, x(s), x' (s)) ds.
Sufficient conditions to guarantee the existence of at least one positive solution are established. The emphasis is put on the one-dimensional p-Laplacian term [Φ(ρ(t)x'(t))]' involved with the nonnegative function ρ satisfying −∞+∞1/ρ(s) ds = +∞.

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