Abstract:
We use a topological method implying the reduction of the initial problem to solving an operational equation in a Hilbert space and consequent calculation of the rotation of the corresponding vector field. We show that in a sphere of a sufficiently large radius the problem has at least one generalized solution.
Citation:
S. N. Timergaliev, I. R. Mavleev, “Solvability of the boundary value problem for a partial quasilinear differential equation of the fourth order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 12, 52–57; Russian Math. (Iz. VUZ), 54:12 (2010), 45–50
\Bibitem{TimMav10}
\by S.~N.~Timergaliev, I.~R.~Mavleev
\paper Solvability of the boundary value problem for a~partial quasilinear differential equation of the fourth order
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 12
\pages 52--57
\mathnet{http://mi.mathnet.ru/ivm7160}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2814578}
\elib{https://elibrary.ru/item.asp?id=15208510}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 12
\pages 45--50
\crossref{https://doi.org/10.3103/S1066369X10120054}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79952856995}
Linking options:
https://www.mathnet.ru/eng/ivm7160
https://www.mathnet.ru/eng/ivm/y2010/i12/p52
This publication is cited in the following 1 articles:
Yue Yu., Tian Yu., Zhang M., Liu J., “Existence of Infinitely Many Solutions For Fourth-Order Impulsive Differential Equations”, Appl. Math. Lett., 81 (2018), 72–78
Citation in format AMSBIB
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