Benchohra, M.; Hamani, S.; Henderson, J. Functional differential inclusions with integral boundary conditions. (English) Zbl 1182.34006 Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 15, 13 p. (2007). Summary: We consider the second order functional differential inclusion\[ x''(t)+\lambda x'(t)\in F(t,x_t)\text{ a.e. }t\in[0,1]\tag{1} \]with initial function values,\[ x(t)=\phi(t),\quad \in[-r,0],\tag{2} \]and integral boundary conditions,\[ x(1)=\int^1_0 g(x(s))\,ds\tag{3} \]where \(F:[0,1]\times C([-r,0],\mathbb R)\to{\mathcal P}(\mathbb R)\) is a compact valued multivalued map, \({\mathcal P}(\mathbb R)\) is the family of all subsets of \(\mathbb R\), \(\lambda <0\), \(\phi\in C([-r,0],\mathbb R)\) and \(g:\mathbb R\to\mathbb R\) is continuous.By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values. Cited in 8 Documents MSC: 34A09 Implicit ordinary differential equations, differential-algebraic equations 34K10 Boundary value problems for functional-differential equations Keywords:boundary value problem; functional differential inclusions; integral boundary conditions; contraction; fixed point PDFBibTeX XMLCite \textit{M. Benchohra} et al., Electron. J. Qual. Theory Differ. Equ. 2007, Paper No. 15, 13 p. (2007; Zbl 1182.34006) Full Text: DOI EuDML EMIS