Global continua of positive solutions for equations with nondifferentiable operators
Existence of global continua of solutions to nonlinear fixed point equations \(x= f(\lambda, x)\), where \(f:[0,+\infty)\times K\to K\) is a completely continuous operator in the cone \(K\), in the sense that the unbounded continuum \(S\) is such that \(S\cap\partial G\neq\emptyset\) for every bounded open set \(G\) containing the origin is studied. The author gives two variants of previous work by Amann, Bahtin and Dancer. In the first case, \(f\) has a monotone minorant and in the second a Hammerstein operator and a priori estimates are involved. An application to periodic solutions of the ordinary differential equation \(-x''= f(x, x')\) under suitable assumptions is also given.
existence of global continua of solutions
scientific article; zbMATH DE number 1384934
scientific article