Jaruszewska-Walczak, Danuta Infinite systems of hyperbolic differential-functional inequalities. (English) Zbl 1103.35100 Zesz. Nauk. Uniw. Jagiell. 1285, Univ. Iagell. Acta Math. 43, 219-228 (2005). Summary: The paper deals with systems of hyperbolic differential-functional inequalities related to initial value problem on the generalized Haar pyramid for equations \[ \partial_tz_\lambda(t,x)=f_\lambda\bigl(t,x,z, \partial_xz_\lambda(t,x)\bigr),\;\lambda\in\Lambda, \] where \((t,x)= (t,x_1,\dots,x_n)\), \(z=\{z_\lambda\}_{\lambda \in\Lambda}\) and \(\Lambda\) is a compact set of indices. A theorem on strong differential-functional inequalities is the main result of the paper. Extremal solutions of initial value problems for infinite systems of ordinary differential-functional equations are used in the proof of a theorem on weak partial differential-functional inequalities. MSC: 35R45 Partial differential inequalities and systems of partial differential inequalities 35R10 Partial functional-differential equations 34K06 Linear functional-differential equations Keywords:strong differential-functional inequalities; ordinary differential-functional equations; weak partial differential-functional inequalities PDFBibTeX XMLCite \textit{D. Jaruszewska-Walczak}, Zesz. Nauk. Uniw. Jagiell., Univ. Iagell. Acta Math. 1285(43), 219--228 (2005; Zbl 1103.35100) Full Text: EuDML