Geodesic
Solvability of the boundary value problem for a~partial quasilinear differential equation of the fourth order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2010), pp. 52-57

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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.
Keywords: operational equation, topological method, vector field rotation, generalized solution, Hilbert space. 
@article{IVM_2010_12_a4,
     author = {S. N. Timergaliev and I. R. Mavleev},
     title = {Solvability of the boundary value problem for a~partial quasilinear differential equation of the fourth order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {52--57},
     publisher = {mathdoc},
     number = {12},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_12_a4/}
}
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S. N. Timergaliev; I. R. Mavleev. Solvability of the boundary value problem for a~partial quasilinear differential equation of the fourth order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2010), pp. 52-57. http://geodesic.mathdoc.fr/item/IVM_2010_12_a4/