Existence for a k-Hessian equation involving supercritical growth

被引：24

作者：

de Oliveira, Jose Francisco ^{[1
]}

do O, Joao Marcos ^{[2
]}

Ubilla, Pedro ^{[3
]}

机构：

[1] Univ Fed Piaui, Dept Math, BR-64049550 Teresina, PI, Brazil

[2] Univ Brasilia, Dept Math, BR-70297400 Brasilia, DF, Brazil

[3] Univ Santiago Chile, Dept Matemat, Casilla 307,Correo 2, Santiago, Chile

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 267卷 / 02期

关键词：

k-Hessian equation; Supercritical growth; Variational methods; DIRICHLET PROBLEM; ELLIPTIC-EQUATIONS;

D O I：

10.1016/j.jde.2019.01.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we use variational techniques to give existence results for the problem {s(k)[u] = f(x, -u) in Omega u < 0 in Omega u = 0 on partial derivative Omega where S-k[u] is the k-Hessian operator and f (x, u) is a supercritical nonlinearity in the sense introduced by [K. Tso, Ann. Inst. Henri Poincare (1990)]. Using some ideas from a celebrated article by Brezis and Nirenberg we show existence of a positive solution considering supercritical nonlinearities, which is surprising given the validity of the Pohozaev identity. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：1001 / 1024

页数：24

共 25 条

[1] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS
BREZIS, H
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) : 437 - 477
[2] THE DIRICHLET PROBLEM FOR NONLINEAR 2ND-ORDER ELLIPTIC-EQUATIONS .3. FUNCTIONS OF THE EIGENVALUES OF THE HESSIAN
CAFFARELLI, L
NIRENBERG, L
SPRUCK, J
[J]. ACTA MATHEMATICA, 1985, 155 (3-4) : 261 - 301
[3] Critical dimension of a Hessian equation involving critical exponent and a related asymptotic result
Chou, KS
Geng, D
Yan, SS
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 129 (01) : 79 - 110
[4] A variational theory of the Hessian equation
Chou, KS
Wang, XJ
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2001, 54 (09) : 1029 - 1064
[5] Clement P., 1996, TOPOL METHOD NONL AN, V7, P133
[6] Bifurcation and admissible solutions for the Hessian equation
Dai, Guowei
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 273 (10) : 3200 - 3240
[7] On a class of quasilinear elliptic problems involving critical exponents
de Figueiredo, DG
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2000, 2 (01) : 47 - 59
[8] Concentration-compactness principle and extremal functions for a sharp Trudinger-Moser inequality
de Oliveira, Jose Francisco
do O, Joao Marcos
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 52 (1-2) : 125 - 163
[9] Critical and subcritical fractional problems with vanishing potentials
do O, Joao Marcos
Miyagaki, Olimpio H.
Squassina, Marco
[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2016, 18 (06)
[10] On supercritical Sobolev type inequalities and related elliptic equations
do O, Joao Marcos
Ruf, Bernhard
Ubilla, Pedro
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 55 (04)

← 1 2 3 →