Differential and Integral Equations

Resonant problems with multidimensional kernel and periodic nonlinearities

A. Cañada and D. Ruiz

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Abstract

In this paper we deal with semilinear boundary value problems for systems of equations whose nonlinear part involves linear combination of periodic functions and such that the linear part has a multidimensional solution space. This kind of problems is very important in applications, specially in mechanics and electric circuits theory. By using the Liapunov-Schmidt reduction and topological degree techniques, together with a careful analysis of the oscillatory behavior of some integrals associated to the bifurcation equation, we give a qualitative and quantitative description of the range of the corresponding nonlinear operator. Also, we provide some multiplicity results.

Article information

Source
Differential Integral Equations, Volume 16, Number 4 (2003), 499-512.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060655

Mathematical Reviews number (MathSciNet)
MR1972877

Zentralblatt MATH identifier
1056.34020

Subjects
Primary: 34B15: Nonlinear boundary value problems
Secondary: 47E05: Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47) 47N20: Applications to differential and integral equations

Citation

Cañada, A.; Ruiz, D. Resonant problems with multidimensional kernel and periodic nonlinearities. Differential Integral Equations 16 (2003), no. 4, 499--512. https://projecteuclid.org/euclid.die/1356060655


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