Advances in Differential Equations

Infinitely many solutions of weakly coupled superlinear systems

Marc Henrard

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Abstract

We study weakly coupled superlinear systems with different boundary conditions. The boundary conditions that we consider are the Sturm-Liouville and the three-point boundary conditions. We first prove a continuation theorem based on coincidence degree and explain how to compute the degree for some simple scalar differential equations. Then we apply those results to prove the existence of infinitely many solutions to the weakly coupled system.

Article information

Source
Adv. Differential Equations Volume 2, Number 5 (1997), 753-778.

Dates
First available in Project Euclid: 22 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366638965

Mathematical Reviews number (MathSciNet)
MR1751426

Zentralblatt MATH identifier
1023.34501

Subjects
Primary: 34B15: Nonlinear boundary value problems
Secondary: 34B10: Nonlocal and multipoint boundary value problems 47H11: Degree theory [See also 55M25, 58C30]

Citation

Henrard, Marc. Infinitely many solutions of weakly coupled superlinear systems. Adv. Differential Equations 2 (1997), no. 5, 753--778. https://projecteuclid.org/euclid.ade/1366638965.


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