Periodic and Boundary Value Problems for Second Order Differential Equations

Proceedings Mathematical Sciences

Nikolaos S Papageorgiou²  Francesca Papalini¹ 

[1] Department of Mathematics, University of Ancona, Via Brecce Bianche, Ancona 0, Italy$$;Department of Mathematics, National Technical University, Zografou Campus, Athens 0, Greece$$

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.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 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.

【 授权许可】

Unknown