Existence of solutions to Sturm–Liouville boundary value problems - Gabriela Mihaylova; Petio Kelevedjiev (Electronic Journal of Qualitative Theory of Differential Equations, 2025)
We study the solvability of Sturm–Liouville boundary value problems for $x''=f(t,x,x'), t\in(0,1)$. The nonlinearity can be defined on a bounded set and is required to be continuous on its subset. The results obtained are based on combinations of well-known conditions with barrier strip type conditions.