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Scalar Steady-State in Population Biology as a Nonlinear Eigenvalue Problem

In: Biomathematics and Related Computational Problems

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  • C. A. Coimbra

    (National Laboratory for Scientific Computation)

Abstract

In this paper we employ the critical point theory to study a scalar steady-state equation occurring in population biology. We treat the equation as an isoperimetric nonlinear eigenvalue problem. We obtain an infinite sequence of positive eigenfunctions by imposing a Z2-symmetry and using an homotopy argument. We also use a Pohozaev type of equality to obtain a necessary and sufficient condition for an eigen function to be related to a positive eigenvalue.

Suggested Citation

  • C. A. Coimbra, 1988. "Scalar Steady-State in Population Biology as a Nonlinear Eigenvalue Problem," Springer Books, in: Luigi M. Ricciardi (ed.), Biomathematics and Related Computational Problems, pages 429-438, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2975-3_38
    DOI: 10.1007/978-94-009-2975-3_38
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