Geodesic
On Nontrivial Solutions of Homogeneous Dirichlet Problem for Partial Differential Equations in a Layer
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 2, p. 193 .

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We establish the necessary and sufficient conditions of existence of nontrivial quasi-polynomial solutions of the problem in a layer for homogeneous partial differential equation with $s+1$ variables of second order in time variable and generally infinite order in other $s$ (spatial) variables with Dirichlet boundary conditions in time. We apply the differential-symbol method for constructing such quasi-polynomial solutions. We also give examples of problems for which we construct other solutions besides of quasi-polynomial ones.
Classification : 35G15 35K05
Keywords: Differential-symbol method, two-point problem for partial differential equations, multipoint problem, equations of mathematical physics 
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     title = {On {Nontrivial} {Solutions} of {Homogeneous} {Dirichlet} {Problem} for {Partial} {Differential} {Equations} in a {Layer}},
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Z. Nytrebych; V. Il; kiv; P. Pukach; O. Malanchuk. On Nontrivial Solutions of Homogeneous Dirichlet Problem for Partial Differential Equations in a Layer. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 2, p. 193 . http://geodesic.mathdoc.fr/item/KJM_2018_42_2_a2/