Geodesic
Boundary value problem for third order equation with multiple characteristics and alternating function on the highest derivative
Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 1, pp. 48-58

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In this paper we investigated the regular solvability of conjugate problem (generalized diffraction problem) for third order equation with multiple characteristics and alternating function on the highest derivative. This function has a discontinuity of the first kind and changes sign when passing the point of discontinuity. The existence and uniqueness of regular solutions are proved by the regularization and continuation methods. 
@article{DVMG_2017_17_1_a4,
     author = {A. I. Kozhanov and S. V. Potapova},
     title = {Boundary value problem for third order equation with multiple characteristics and alternating function on the highest derivative},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {48--58},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2017_17_1_a4/}
}
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A. I. Kozhanov; S. V. Potapova. Boundary value problem for third order equation with multiple characteristics and alternating function on the highest derivative. Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 1, pp. 48-58. http://geodesic.mathdoc.fr/item/DVMG_2017_17_1_a4/