Djebali, Smaïl; Kavian, Otared; Moussaoui, Toufik Qualitative properties and existence of solutions for a generalized Fisher-like equation. (English) Zbl 1301.34020 Iran. J. Math. Sci. Inform. 4, No. 2, 65-81 (2009). 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. Cited in 5 Documents 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 Keywords:linear and sub-linear ODEs; variational method; fixed point theorems; compactness criterion PDFBibTeX XMLCite \textit{S. Djebali} et al., Iran. J. Math. Sci. Inform. 4, No. 2, 65--81 (2009; Zbl 1301.34020) Full Text: Link