A global characterization of the Fu?ík spectrum for a system of ordinary differential equations |
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| Authors: | Eugenio Massa Bernhard Ruf |
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| Institution: | a Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil
b Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy |
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| Abstract: | The Fu?ík spectrum for systems of second order ordinary differential equations with Dirichlet or Neumann boundary values is considered: it is proved that the Fu?ík spectrum consists of global C1 surfaces, and that through each eigenvalue of the linear system pass exactly two of these surfaces. Further qualitative, asymptotic and symmetry properties of these spectral surfaces are given. Finally, related problems with nonlinearities which cross asymptotically some eigenvalues, as well as linear-superlinear systems are studied. |
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| Keywords: | Systems of ordinary differential equations Fu?í k spectrum for systems Symmetry properties |
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