## Related Articles

- A Remark on the Existence of a Periodic Solution. Filippov, V. V. // Differential Equations;Mar2003, Vol. 39 Issue 3, p462
Discusses the development of methods for studying differential equations and inclusions with discontinuous right-hand side. Generalization of the results of the classical theory; Theory of the Cauchy problem for equations and inclusions with discontinuous right-hand side; Modification of the...

- Inverse problem for Euler-Poisson-Darboux abstract differential equation. Glushak, A. V.; Popova, V. A. // Journal of Mathematical Sciences;Mar2008, Vol. 149 Issue 4, p1453
For the nonhomogeneous Euler-Poisson-Darboux equation in a Banach space, we consider the problem of determination of a parameter on the right-hand side of the equation by the excessive final condition. This problem can be reduced to the inversion of some operator represented in a suitable form...

- A Remark on the Existence Interval of the Solution of the Cauchy Problem. Filippov, V. V. // Differential Equations;Aug2004, Vol. 40 Issue 8, p1205
Focuses on the development of methods for studying equations and inclusions with discontinuous right-hand side. Estimated length of the existence interval for the solution of the Cauchy problem for the equation; Use of the principle of continuation with respect to a parameter; Application of...

- Darboux transformations for the generalized SchrÃ¶dinger equation. Suzko, A. A.; Giorgadze, G. // Physics of Atomic Nuclei;Mar2007, Vol. 70 Issue 3, p607
The intertwining operator technique is applied to the SchrÃ¶dinger equation with an additional functional dependence h( r) on the right-hand side of the equation. The suggested generalized transformations turn into the Darboux transformations for both fixed and variable values of energy and...

- On Shifts along Trajectories. Filippov, V. V. // Mathematical Notes;Jul/Aug2003, Vol. 74 Issue 1/2, p266
The extension of the theory of boundary-value problems to ordinary differential equations and inclusions with discontinuous right-hand sides based on the construction of a new version of the method of shifts along trajectories is continued.

- Nonlinear Goursat-Darboux control problem: Conditions for the preservation of global solvability. Lisachenko, I. V.; Sumin, V. I. // Differential Equations;Jun2011, Vol. 47 Issue 6, p863
We consider the nonlinear vector Goursat-Darboux problem of general form with a control on the right-hand side in the differential equation. We consider the case in which its solution necessarily belongs to the class of functions with p-integrable (for some p > 1) mixed and first partial...

- Asymptotic expansion of singular solutions to Protter problem for (2+1)-D degenerate wave equation. Nikolov, Aleksey; Popivanov, Nedyu // AIP Conference Proceedings;Dec2013, Vol. 1570 Issue 1, preceding p249
We consider some boundary value problems for a weakly hyperbolic equation, which are three-dimensional analogues of the Darboux problems on the plain. These problems arise in transonic fluid dynamics and they are introduced by Protter in 1952. As distinct from the planar Darboux problems, the...

- Riemann-Hadamard function for Darboux-Goursat problem and its multidimensional application. Nikolov, Aleksey; Popivanov, Nedyu // AIP Conference Proceedings;2014, Vol. 1631, p175
We consider a planar Darboux-Goursat problem with singular coefficients. It is known that its unique solution (which is not a solution in the classical sense) may have strong power type singularity isolated at one boundary point even for very smooth functions in the right-hand side of the...

- Exact Asymptotic Expansion of Singular Solutions for the (2 + 1)-D Protter Problem. Dechevski, Lubomir; Popivanov, Nedyu; Popov, Todor // Abstract & Applied Analysis;2012, p1
We study three-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of the Darboux problems in R2. In contrast to the planar Darboux problem the three-dimensional version is not well posed, since its homogeneous adjoint problem has an infinite number of...

- Analysis of Singularities of Solutions to Protter Problems for the Wave Equation. Popivanov, Nedyu; Popov, Todor // AIP Conference Proceedings;2014, Vol. 1637, p824
We study four-dimensional boundary value problems for the nonhomogeneous wave equation, which are analogues of Darboux problems on the plane. They were formulated by M.H.Protter in connection with BVPs for mixed type equations that model transonic flow phenomena. It is known that the unique...