Differential and Integral Equations

Resonant problems with multidimensional kernel and periodic nonlinearities

A. Cañada and D. Ruiz

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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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