In this paper, we deal with a transmission problem for a class of quasilinear pseudoparabolic equations. Existence, uniqueness and continuous dependence of the solution upon the data are obtained via the Rothe method. Moreover, the convergence of the method and an error estimate of the approximations are established.

Sufficient conditions are established for the asymptotic behavior of a third-order nonlinear differential equation. Our results improve on Qian’s [C. Qian, Asymptotic behavior of a third-order nonlinear differential equation, J. Math. Anal. Appl., 284 (2003), 191–205]

In this study the third order nonlinear susceptibilities are theoreticallycalculated for an electron confined in an isolated PbS/ CdSe/ CdS spherical core-shellshellquantum dots. Our calculation is associated with intersubband transitions in theconduction band. We used the effective mass approximation in this study which is asimple and straightforward study of the third-order optical nonlineari...

Equations of mixed type, the degeneracy line which is envelope a family characteristics, therefore, itself also characteristic, in literature it customary to call equations type second kind, causes additional difficulties study boundary value problems for kind. In present work, problem homogeneous equation parabolic-hyperbolic third order kind investigated. Necessary and sufficient conditions e...

The article considers third-order equations with multiple characteristics general boundary value conditions and non-local initial data. A regular solution to the problem known methods is constructed here. uniqueness of proved by method energy integrals. This uses theory non-negative quadratic forms. existence a reducing Fredholm integral second kind. In this case, Green’s function potential used.