Ntouyas, Sotiris K. Neumann boundary value problems for impulsive differential inclusions. (English) Zbl 1195.34041 Electron. J. Qual. Theory Differ. Equ. 2009, Spec. Iss. I, Paper No. 22, 13 p. (2009). From the text: This paper is concerned with the existence of solutions of boundary value problems (BVP for short) for second order differential inclusions with Neumann boundary. We consider the second order impulsive Neumann BVP,\[ x''(t)+k^2x(t)\in F(t,x(t)),\text{ a.e. }t\in J':=[0,1]\setminus \{t_1,\dots,t_m\}, \]\[ \Delta x'|_{t=t_k}=I_k(x(t^-_k)),\quad k=1,\dots,m, \]\[ x'(0) = x'(1) = 0, \]where \(F : [0, 1]\times \mathbb R\to{\mathcal P}(\mathbb R)\) is a compact valued multivalued map, \({\mathcal P}(\mathbb R)\) is the family of all subsets of \(\mathbb R\), \(k\in (0,\frac\pi2)\), \(0<t_1<t_2<\cdots <t_m<1\), \(I_k\in C(\mathbb R,\mathbb R)\) \((k=1,2,\dots,m)\), \(\Delta xl_{t=t_k}=x(t^+_k)-x(t^-_k)\), \(x(t^+_k)\) and \(x(t^-_k)\) represent the right and left limits of \(x(t)\) at \(t=t_k\) respectively, \(k=1,2,\dots,m\).By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values. Cited in 4 Documents MSC: 34B37 Boundary value problems with impulses for ordinary differential equations 34A60 Ordinary differential inclusions 47N20 Applications of operator theory to differential and integral equations Keywords:Neumann boundary value problem; differential inclusions; fixed point PDFBibTeX XMLCite \textit{S. K. Ntouyas}, Electron. J. Qual. Theory Differ. Equ. 2009, Paper No. 22, 13 p. (2009; Zbl 1195.34041) Full Text: DOI EuDML EMIS