Dancer, E. N.; Du, Yihong Competing species equations with diffusion, large interactions, and jumping nonlinearities. (English) Zbl 0815.35024 J. Differ. Equations 114, No. 2, 434-475 (1994). In this paper a reaction-diffusion system of the form \[ - \Delta u = au - u^ 2 - cuv, \quad - \Delta u = dv - v^ 2 - euv \quad \text{in} \quad D \subset \mathbb{R}^ n \] with homogeneous Dirichlet boundary conditions is studied. \(a,c,d,e\) are positive constants. The authors study the asymptotic behavior of the positive solution as the parameters \(c,e\) tend to infinity. Reviewer: R.Sperb (Zürich) Cited in 1 ReviewCited in 62 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B40 Asymptotic behavior of solutions to PDEs 35K57 Reaction-diffusion equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:jumping nonlinearities; asymptotic behavior of positive solution PDFBibTeX XMLCite \textit{E. N. Dancer} and \textit{Y. Du}, J. Differ. Equations 114, No. 2, 434--475 (1994; Zbl 0815.35024) Full Text: DOI