EXISTENCE RESULTS AND A PRIORI ESTIMATES FOR SOLUTIONS OF QUASILINEAR PROBLEMS WITH GRADIENT TERMS

被引：5

作者：

Filippucci, Roberta ^{[1
]}

Lini, Chiara ^{[1
]}

机构：

[1] Univ Perugia, Dipartimento Matemat & Informat, Via Vanvitelli 1, I-06123 Perugia, Italy

来源：

OPUSCULA MATHEMATICA | 2019年 / 39卷 / 02期

关键词：

existence result; quasilinear problems; a priori estimates; NONLINEAR ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; LOCAL BEHAVIOR; REGULARITY; CONVECTION;

D O I：

10.7494/OpMath.2019.39.2.195

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we establish a priori estimates and then an existence theorem of positive solutions for a Dirichlet problem on a bounded smooth domain in R-N with a nonlinearity involving gradient terms. The existence result is proved with no use of a Liouville theorem for the limit problem obtained via the usual blow up method, in particular we refer to the modified version by Ruiz. In particular our existence theorem extends a result by Lorca and Ubilla in two directions, namely by considering a nonlinearity which includes in the gradient term a power of u and by removing the growth condition for the nonlinearity f at u = 0.

引用

页码：195 / 206

页数：12

共 33 条

[1] A priori estimates and continuation methods for positive solutions of p-Laplace equations [J].