POSITIVE SOLUTIONS OF A NONLOCAL AND NONVARIATIONAL ELLIPTIC PROBLEM

被引：0
|
作者：
Liu, Lingjun [1 ]
Shi, Feilin [2 ]
机构：
[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
[2] Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2021年 / 41卷 / 05期
基金：
中国国家自然科学基金;
关键词：
positive solutions; nonvariational elliptic problem; a priori estimates; A-PRIORI BOUNDS; EQUATIONS; EXISTENCE;
D O I：
10.1007/s10473-021-0522-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we will study the nonlocal and nonvariational elliptic problem {-(1 + alpha parallel to u parallel to(alpha q)(q))Delta u = vertical bar u vertical bar(p-1) u + h(x, u, del u) in Omega, u = 0 on partial derivative Omega, (0,1) where a > 0, alpha > 0, 1 < q < 2*, p is an element of (0, 2* - 1) \ {1} and Omega is a bounded smooth domain in R-N (N >= 2). Under suitable assumptions about h(x, u, del u), we obtain a priori estimates of positive solutions for the problem (0.1). Furthermore, we establish the existence of positive solutions by making use of these estimates and of the method of continuity.
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页码：1764 / 1776
页数：13
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