Nonlinear p(x)-Elliptic Equations in General Domains

被引：1

作者：

Azroul, Elhoussine ^{[1
]}

Khouakhi, Moussa ^{[1
]}

Yazough, Chihab ^{[2
]}

机构：

[1] Dhar El Mahraz Sidi Mohamed Ben Abdellah Univ, Fac Sci, Lab Math Anal & Applicat, Atlas Fes 1796, Morocco

[2] Sidi Mohamed Ben Abdellah Univ, Fac Polydisciplinary Taza, LSI, BP 1223, Fes, Morocco

来源：

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2022年 / 30卷 / 03期

关键词：

Sobolev spaces with variable exponents; Strongly nonlinear elliptic equations; Unbounded domains; Existence results; Boundedness of solutions; ELLIPTIC-EQUATIONS; NATURAL GROWTH; VARIATIONAL-PROBLEMS; VARIABLE EXPONENT; EXISTENCE; REGULARITY;

D O I：

10.1007/s12591-018-0433-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we prove an existence result and some regularity for the solution of the strongly nonlinear p(x)-elliptic problem of the form: - div a(x , u, Vu) + c(x, u)+ H(x, u, Vu) = f(x) - div g(x) in Omega, u is an element of W-0(1,p(.)) (Omega), where H(x, s, xi) and c(x, s) are a nonlinear terms satisfying some growth condition but no sign condition on H. The assumptions on the source terms load to the existence of solutions. The domain Omega is allowed to have infinite Lebesgue measure.

引用

页码：607 / 630

页数：24

共 28 条

[1]

Azroul E., 2013, Electron. J. Differ. Equ, V68, P1

[2] Entropy and Renormalized Solutions for Nonlinear Elliptic Problem Involving Variable Exponent and Measure Data [J].

Benboubker, Mohamed Badr ;

Chrayteh, Houssam ;

El Moumni, Mostafa ;

Hjiaj, Hassane .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2015, 31 (01) :151-169

[3] L-INFINITY ESTIMATE FOR SOME NONLINEAR ELLIPTIC PARTIAL-DIFFERENTIAL EQUATIONS AND APPLICATION TO AN EXISTENCE RESULT [J].

BOCCARDO, L ;

MURAT, F ;

PUEL, JP .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1992, 23 (02) :326-333

[4]

Cupini G, 2014, ADV DIFFERENTIAL EQU, V19, P693

[5]

Dall'aglio A, 2005, BOLL UNIONE MAT ITAL, V8B, P653

[6] Nonlinear elliptic equations with natural growth in general domains [J].

Dall'Aglio, A. ;

Giachetti, D. ;

Puel, J. -P. .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2002, 181 (04) :407-426

[7] Existence of bounded solutions for nonlinear elliptic equations in unbounded domains [J].

Dall'Aglio, A ;

De Cicco, V ;

Giachetti, D ;

Puel, JP .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2004, 11 (04) :431-450

[8] Lebesgue and Sobolev Spaces with Variable Exponents [J].

Diening, Lars ;

Harjulehto, Petteri ;

Hasto, Peter ;

Ruzicka, Michael .

LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 :1-+

[9]

Duan L, 2014, ELECTRON J QUAL THEO, P1

[10] QUASILINEAR ELLIPTIC PROBLEMS IN UNBOUNDED DOMAINS [J].

EDMUNDS, DE ;

WEBB, JRL .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1973, 334 (1598) :397-410

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