Differential and Integral Equations
- Differential Integral Equations
- Volume 16, Number 4 (2003), 499-512.
Resonant problems with multidimensional kernel and periodic nonlinearities
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.
Differential Integral Equations, Volume 16, Number 4 (2003), 499-512.
First available in Project Euclid: 21 December 2012
Permanent link to this document
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