A QUASI-LINEAR NONLOCAL VENTTSEL' PROBLEM OF AMBROSETTI-PRODI TYPE ON FRACTAL DOMAINS

被引：8

作者：

Lancia, Maria Rosaria ^{[1
]}

Velez-Santiago, Alejandro ^{[2
]}

Vernole, Paola ^{[1
]}

机构：

[1] Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Via A Scarpa 16, I-00161 Rome, Italy

[2] Univ Puerto Rico, Dept Math Sci, Mayaguez, PR 00681 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 08期

关键词：

Venttsel' boundary conditions; Koch snowflake domain; weak solutions; a priori estimates; sub-supersolution method; Leray-Schauder degree theory; ELLIPTIC-EQUATIONS; NEUMANN PROBLEM; SOBOLEV SPACES; BOUNDARY; APPROXIMATION; OPERATORS; FORM;

D O I：

10.3934/dcds.2019184

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the solvability of the Ambrosetti-Prodi problem for the p-Laplace operator Delta(p), with Venttsel' boundary conditions on a two-dimensional open bounded set with Koch-type boundary, and on an open bounded three-dimensional cylinder with Koch-type fractal boundary. Using a priori estimates, regularity theory and a sub-supersolution method, we obtain a necessary condition for the non-existence of solutions (in the weak sense), and the existence of at least one globally bounded weak solution. Moreover, under additional conditions, we apply the Leray-Schauder degree theory to obtain results about multiplicity of weak solutions.

引用

页码：4487 / 4518

页数：32