Open Access
2003 Resonant problems with multidimensional kernel and periodic nonlinearities
A. Cañada, D. Ruiz
Differential Integral Equations 16(4): 499-512 (2003). DOI: 10.57262/die/1356060655


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.


Download Citation

A. Cañada. D. Ruiz. "Resonant problems with multidimensional kernel and periodic nonlinearities." Differential Integral Equations 16 (4) 499 - 512, 2003.


Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1056.34020
MathSciNet: MR1972877
Digital Object Identifier: 10.57262/die/1356060655

Primary: 34B15
Secondary: 47E05 , 47N20

Rights: Copyright © 2003 Khayyam Publishing, Inc.

Vol.16 • No. 4 • 2003
Back to Top