On the number of positive solutions of nonlinear systems

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155 Citations (Scopus)

Abstract

We prove that appropriate combinations of superlinearity and sublinearity of f(u) with respect to Φ at zero and infinity guarantee the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system (Φ(u′) ′ + λh(t)f(u) = 0, 0 < t < 1. The vector-valued function Φ is defined by Φ(u′) = ( (u1′ ,..., (un′)), where u = (u1,...,un and covers the two important cases (u′) = u′ and (u′) = u′ p-2u′, p > 1. Our methods employ fixed point theorems in a cone.

Original language English (US) 287-306 20 Journal of Mathematical Analysis and Applications 281 1 Published - May 1 2003

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Boundary value problems
Nonexistence
Fixed point theorem
Cones
Nonlinear systems
Positive Solution
n-dimensional
Multiplicity
Cone
Nonlinear Systems
Boundary Value Problem
Infinity
Zero

ASJC Scopus subject areas

• Analysis
• Applied Mathematics

Cite this

In: Journal of Mathematical Analysis and Applications, Vol. 281, No. 1, 01.05.2003, p. 287-306.

Research output: Contribution to journalArticle

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