Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities

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Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities. / Pavlenko, V. N.; Potapov, D. K.

In: Mathematical Notes, Vol. 110, No. 1-2, 01.07.2021, p. 226-241.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{ed47dc6ec95d4916a5b81fea74d384bd,

title = "Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities",

abstract = "Abstract: For elliptic systems with discontinuous nonlinearities, we study the existence of strong solutions whose values are points of continuity with respect to the state variables for almost all values of the spatial variable. Such solutions are said to be semiregular. An upper-and-lower-solution principle is established for the existence of semiregular solutions to elliptic systems with discontinuous nonlinearities. This principle is used to prove theorems on the existence of semiregular solutions of elliptic systems with discontinuous nonlinearities, in particular, nontrivial solutions of problems with a parameter. Examples of classes of nonlinearities with separated variables satisfying the conditions of our theorems are given.",

keywords = "discontinuous nonlinearity, elliptic system, lower solution, semiregular solution, upper solution, PARTIAL-DIFFERENTIAL EQUATIONS",

author = "Pavlenko, {V. N.} and Potapov, {D. K.}",

note = "Pavlenko, V.N., Potapov, D.K. Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities. Math Notes 110, 226–241 (2021). https://doi.org/10.1134/S0001434621070245",

year = "2021",

month = jul,

day = "1",

doi = "10.1134/s0001434621070245",

language = "English",

volume = "110",

pages = "226--241",

journal = "Mathematical Notes",

issn = "0001-4346",

publisher = "Pleiades Publishing",

number = "1-2",

}

RIS

TY - JOUR

T1 - Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities

AU - Pavlenko, V. N.

AU - Potapov, D. K.

N1 - Pavlenko, V.N., Potapov, D.K. Existence of Semiregular Solutions of Elliptic Systems with Discontinuous Nonlinearities. Math Notes 110, 226–241 (2021). https://doi.org/10.1134/S0001434621070245

PY - 2021/7/1

Y1 - 2021/7/1

N2 - Abstract: For elliptic systems with discontinuous nonlinearities, we study the existence of strong solutions whose values are points of continuity with respect to the state variables for almost all values of the spatial variable. Such solutions are said to be semiregular. An upper-and-lower-solution principle is established for the existence of semiregular solutions to elliptic systems with discontinuous nonlinearities. This principle is used to prove theorems on the existence of semiregular solutions of elliptic systems with discontinuous nonlinearities, in particular, nontrivial solutions of problems with a parameter. Examples of classes of nonlinearities with separated variables satisfying the conditions of our theorems are given.

AB - Abstract: For elliptic systems with discontinuous nonlinearities, we study the existence of strong solutions whose values are points of continuity with respect to the state variables for almost all values of the spatial variable. Such solutions are said to be semiregular. An upper-and-lower-solution principle is established for the existence of semiregular solutions to elliptic systems with discontinuous nonlinearities. This principle is used to prove theorems on the existence of semiregular solutions of elliptic systems with discontinuous nonlinearities, in particular, nontrivial solutions of problems with a parameter. Examples of classes of nonlinearities with separated variables satisfying the conditions of our theorems are given.

KW - discontinuous nonlinearity

KW - elliptic system

KW - lower solution

KW - semiregular solution

KW - upper solution

KW - PARTIAL-DIFFERENTIAL EQUATIONS

UR - http://www.scopus.com/inward/record.url?scp=85113802035&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/793aae62-fedf-370a-b2e9-9b9564d90964/

U2 - 10.1134/s0001434621070245

DO - 10.1134/s0001434621070245

M3 - Article

AN - SCOPUS:85113802035

VL - 110

SP - 226

EP - 241

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -

ID: 85468294