Open AccessNonlinear sixth order models with nonsmooth solutions and monoton nonlinearity
Author(s) -
Elena A Borodina,
С. А. Шабров,
Марина Вячеславовна Шаброва
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1479/1/012023
Subject(s) - mathematics , uniqueness , nonlinear system , pointwise , boundary value problem , mathematical analysis , operator (biology) , cone (formal languages) , interval (graph theory) , continuous function (set theory) , function (biology) , combinatorics , physics , algorithm , biochemistry , chemistry , repressor , quantum mechanics , evolutionary biology , biology , transcription factor , gene
The sixth-order nonlinear spectral problem with nonsmooth solutions is studied. It is proved that the set of non-negative values for which the nonlinear spectral problem has at least one non-trivial non-negative solution is nonempty and coincides with a certain interval. We use the pointwise approach proposed by Yu. V. Pokorny analyzing solutions to a boundary value problem. This approach shown to be effective in the study of the second-order problems. Based on the previously obtained estimates of the Green’s function of the boundary-value problem, it was possible to show that the operator inverting the studied nonlinear problem, representable as a superposition of completely continuous and continuous operators, acts from the cone of nonnegative continuous functions to a narrower set. The last fact allows us to prove the uniqueness of a solution of a nonlinear boundary value problem using the theory of spaces with a cone.