Upper and lower solutions and multiplicity results
Using the topological degree theory, the author obtains some multiplicity results for the second-order differential equation \(x''=f(t,x,x')\), with both linear (periodic and Neumann) and nonlinear boundary conditions. Here, \(f:[a,b]\times \mathbb{R}^2 \to \mathbb{R}\) is continuous and satisfies certain growth conditions. The results extend those from a previous paper by the author, established for \(f\) bounded [J. Math. Anal. Appl. 234, No. 1, 311-327 (1999)].
scientific article; zbMATH DE number 1496303