TY - JOUR

T1 - Semiregular solutions of elliptic boundary-value problems with discontinuous nonlinearities of exponential growth

AU - Pavlenko, V.N.

AU - Potapov, D.K.

PY - 2022

Y1 - 2022

N2 - An elliptic boundary-value problem with discontinuous nonlinearity of exponential growth at infinity is investigated. The existence theorem for a weak semiregular solution of this problem is deduced by the variational method. The semiregularity of a solution means that its values are points of continuity of the nonlinearity with respect to the phase variable almost everywhere in the domain where the boundary-value problem is considered. The variational approach used is based on the concept of a quasipotential operator, unlike the traditional approach, which uses Clarke's generalized derivative

AB - An elliptic boundary-value problem with discontinuous nonlinearity of exponential growth at infinity is investigated. The existence theorem for a weak semiregular solution of this problem is deduced by the variational method. The semiregularity of a solution means that its values are points of continuity of the nonlinearity with respect to the phase variable almost everywhere in the domain where the boundary-value problem is considered. The variational approach used is based on the concept of a quasipotential operator, unlike the traditional approach, which uses Clarke's generalized derivative

KW - elliptic boundary-value problem

KW - discontinuous nonlinearity

KW - exponential growth

KW - semiregular solution

KW - variational method

UR - https://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sm&paperid=9655&option_lang=eng

M3 - Article

VL - 213

SP - 1004

EP - 1019

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 7

ER -