¹Harvey Mudd College, Claremont, USA. Email: castro@math.hmc.edu
²UTSA, San Antonio, USA. Email: chen.chang@utsa.edu

We characterize the \it Fucik spectrum (see [7]) of a class selfadjoint operators. Our characterization relies on Lyapunov-Schmidt reduction arguments. We use this characterization to establish the existence of solutions for a semilinear wave equation. This work has been motivated by the authors results in [4] where one dimensional second order ordinary differential equations are studied.

Key words: Fucik spectrum, Saddle point principle, Asymptotic behavior.

Se caracteriza el espectro de Fucik (véase [7]) de una clase de operadores autoadjuntos. Basamos esta caracterización en el método de reducción de Lyapunov-Schmidt. Usamos esta caracterización para demostrar la existencia de soluciones a una ecuación de onda semilineal. Este trabajo ha sido motivado por los resultados de los autores en [4] donde se estudian ecuaciones diferenciales ordinarias de segundo orden.

Palabras clave: Espectro de Fucik, principio de puntos de silla, comportamiento asintótico.

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References

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