On S-shaped bifurcation curves for multiparameter positone problems
This paper is devoted to the study of the existence of multiple positive solutions of the two-point boundary value problem \(-U''(x)= \lambda f(U(x))\), \(0< x< 1\), \(U(0)= 0= U(1)+ \alpha U'(1)\), where \(\lambda> 0\), \(\alpha> 0\), and \(f\) is a smooth function with \(f> 0\) on \([0,r]\) for some \(r\in (0,+\infty)\). The authors consider the case when \(f\) is initially convex and then concave. Finally, they apply their results to nonlinearities arising in combustion theory and in chemical theory.
existence of multiple positive solutions
scientific article; zbMATH DE number 720451