Luisa Malaguti & Cristina Marcelli
In this paper we investigate the boundary eigenvalue problem
depending on the real parameter . We take continuous and positive and assume that is bounded and becomes active and positive only when exceeds a threshold value . At the point we allow to have a jump. Additional monotonicity properties are required, when needed. Our main discussion deals with the non-autonomous case. In this context we prove the existence of a continuum of values for which this problem is solvable and we estimate the interval of such admissible values. In the autonomous case, we show its solvability for at most one . In the special case when reduces to with continuous, we also give a non-existence result, for any real . Our methods combine comparison-type arguments, both for first and second order dynamics, with a shooting technique. Some applications of the obtained results are included.
Submitted April 15, 2003. Published November 28, 2003.
Math Subject Classifications: 34B40, 34B18, 34C37.
Key Words: Boundary eigenvalue problems, positive bounded solutions, shooting method
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| Luisa Malaguti |
Department of Engineering Sciences and Methods
University of Modena and Reggio Emilia
via Fogliani 1 - 42100 Reggio Emilia, Italy
| Cristina Marcelli |
Department of Mathematical Sciences
Polytechnic University of Marche
via Brecce Bianche - 60131 Ancona, Italy
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