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Qualitative properties and existence of solutions for a generalized Fisher-like equation. (English) Zbl 1301.34020
Summary: This paper is devoted to the study of an eigenvalue second order differential equation, supplied with homogenous Dirichlet conditions and set on the real line. In the linear case, the equation arises in the study of a reaction-diffusion system involved in disease propagation throughout a given population. Under some relations upon the real parameters and coefficients, we present some existence and nonexistence results. We use a variational method and fixed point arguments.

MSC:
34B05 Linear boundary value problems for ordinary differential equations
34B40 Boundary value problems on infinite intervals for ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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