The method of upper and lower solutions for second order differential inclusions with integral boundary conditions (Q968572)

The authors study a class of nonlinear boundary value problems for second order differential inclusions. In particular, they consider the problem \[ x''(t)+\lambda x'(t)\in F(t,x(t)) \text{ a.e. on } T=[0,1], \] \[ x(0)=a, \quad x(1)=\displaystyle{\int_0^1 g(x(s))\,ds}, \] where \(F:[0,1]\times \mathbb R \to 2^{\mathbb R}\) is a Carathéodory multivalued map with non empty, compact and convex values, \(\lambda>0\), \(a\in\mathbb R\) and \(g:\mathbb R \to \mathbb R\) is a continuous and nondecreasing function. By using fixed point techniques combined with the method of lower and upper solutions, the authors prove an existence result.