evolutionary differential-difference equations
An operator approach to the investigation of potentiality of some differential-difference equations
The authors consider a class of evolutionary differential-difference operator equations of the form NEWLINE\[NEWLINEN(u)\equiv P_{2u,t}u_{tt}+P_{1u,t}u_t+Q(t,u)=0_V,NEWLINE\]NEWLINE NEWLINE\[NEWLINE u\in D(N)\subseteq U\subseteq V,\;t\in[t_0,t_1].NEWLINE\]NEWLINE Existence results of variational formulations for the equations are obtained using an operator approach. Then a partial differential-difference equation is given to illustrate the results.
scientific article; zbMATH DE number 6225581