The degree method for condensing operators in periodic boundary value problems (Q5957794)

The method of upper and lower solutions is combined in this paper with penalty and truncation techniques and with Leray-Schauder degree theory to produce conditions for the existence of solutions to the following periodic BVP NEWLINE\[NEWLINE(x'(t)+g(t,x(t),x'(t)))'= f(t,x(t),x'(t)),\quad x(0)=x(T),\;x'(0)=x'(T), NEWLINE\]NEWLINE where \(T>0\) is given, \(g\in C^0([0,T]\times\mathbb R^2)\) is \(T\)-periodic in the first variable and \(f\) satisfies the local Carathéodory conditions on \([0,T]\times\mathbb R^2\). An example of a class of problems as above is provided to illustrate the applicability of the conditions.