Existence of solutions to the nonlinear, singular second order Bohr boundary value problems
This paper studies the existence of solutions and a priori bounds to the boundary value problem \[ \frac{1}{p(t)}(p(t){\mathbf y'}(t))'=q(t){\mathbf f}(t,{\mathbf y}(t),p(t){\mathbf y'}(t)),\;t\in(0,T), \] \[ {\mathbf y}(0)={\mathbf c},\;\int_0^T\frac{ds}{p(s)}\lim_{t\to T^-}p(t){\mathbf y'}(t)-{\mathbf y}(T)={\mathbf d}, \] where \(p\in C([0,T];R)\cap C^1((0,T);R)\) and \(q\in C((0,T);R)\) are positive on \((0,T)\), \({\mathbf f}\in C([0,T]\times R^n\times R^n; R^n),\) and \(\mathbf {c,d}\in R^n\) are constants. As the author writes in the abstract ``The methodology in this paper uses an alternative and equivalent BVP, which is in the class of resonant singular BVPs, and thus this paper obtains novel results by implementing an innovative differential inequality, Lyapunov functions and topological techniques.''
scientific article; zbMATH DE number 6698079
scientific article