Existence principles for higher-order nonlocal boundary-value problems and their applications to singular Sturm-Liouville problems

• Date: 2008
• Main Authors: Staněk, S., Станєк, С.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3153
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

The paper presents existence principles for the nonlocal boundary-value problem $$ (\phi (u^(p-1)))' = g(t, u,...,u^{(p-1)}), \alpha_k(u)=0, 1 \leq k \leq p-1$$ where $p\geq2,\quad \phi: {\mathbb R}\rightarrow{\mathbb R}$ is an increasing and odd homeomorphism, $g$ is a Caratheodory functi...