Periodic and boundary value problems for second order differential equations

被引：5
|
作者：
Papageorgiou, NS
Papalini, F
机构：
[1] Natl Tech Univ, Dept Math, Athens 15780, Greece
[2] Univ Ancona, Dept Math, I-60131 Ancona, Italy
来源：
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2001年 / 111卷 / 01期
关键词：
upper solution; lower solution; order interval; truncation map; penalty function; Caratheodory function; Sobolev space; compact embedding; Dunford-Pettis theorem; Arzela-Ascoli theorem; extremal solution; periodic problem; Sturm-Liouville boundary conditions;
D O I：
10.1007/BF02829543
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study second order scalar differential equations with Sturm-Liouville and periodic boundary conditions. The vector field f(t,x,y) is Caratheodory and in some instances the continuity condition on x or y is replaced by a monotonicity type hypothesis. Using the method of upper and lower solutions as well as truncation and penalization techniques, we show the existence of solutions and extremal solutions in the order interval determined by the upper and lower solutions. Also we establish some properties of the solutions and of the set they form.
引用
收藏
页码：107 / 125
页数：19
相关论文
共 50 条
12345