We have described the set of solutions of a homogeneous system of partial differential equations of the second order in time and, in general, of infinite order in space variables, which satisfy homogeneous local two-point in time conditions. We have studied the cases where a two-point problem has only the trivial solution and where it has nontrivial solutions of the quasipolynomial form. We have also proposed a method of constructing such solutions.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 4, pp. 7–17, October–December, 2009.
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Kalenyuk, P.I., Kohut, I.V. & Nytrebych, Z.M. An investigation into a problem with homogeneous local two-point conditions for a homogeneous system of partial differential equations. J Math Sci 174, 121–135 (2011). https://doi.org/10.1007/s10958-011-0285-y
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DOI: https://doi.org/10.1007/s10958-011-0285-y