Elliptic Problems with Nonlocal Potential Arising in Models of Nonlinear Optics

Hyperbolic differential-difference equations with nonlocal potentials

“…10], in which the solutions are treated in the sense of generalized functions. On the base of (2.6) and arguing as in [14], [15], we prove the following statement.…”

“…In unbounded domains, problems for parabolic [11] and elliptic differential-difference equations [12]- [16] were studied in details. In particular, works [14], [15] were devoted to strongly elliptic equations with nonlocal potentials in one of spatial variables arising in models of nonlinear optics. Hyperbolic differential-difference equations were earlier studied for the case, when the shift operators in the equation acts in the time [17].…”

Inverse problems for Dirac operators with constant delay: uniqueness, characterization, uniform stability

“…Classical methods for solving inverse problems for differential operators [15][16][17][18][19][20][21][22][23][24][25] are not applicable for operators with delay as well as for other classes of nonlocal operators. However, they are often more adequate for modelling various physical processes frequently possessing a nonlocal nature [26][27][28][29][30][31][32].…”

“…are fulfilled. To these w1 (x) and w2 (x), via formulae (31) and (32) there correspond another pair of functions p(x) and q(x) such that (p, q) = (p, q). Then, analogously to the above, relations (28), (35) and (36) will mean that {λ n k,1 ,1 } k∈Z and {λ n k,2 ,2 } k∈Z are subspectra also of the problems B 1,1 ( Q) and B 1,2 ( Q), respectively, with Q = Q.…”

Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

“…Operational methods are applicable to elliptic differential-difference equations as well. At the moment, the following results are obtained (see [46][47][48][49]).…”