Advances in Differential Equations

Infinitely many solutions of weakly coupled superlinear systems

Marc Henrard

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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

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

First available in Project Euclid: 22 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Henrard, Marc. Infinitely many solutions of weakly coupled superlinear systems. Adv. Differential Equations 2 (1997), no. 5, 753--778.

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