Even order nonlinear eigenvalue problems on a measure chain

✍ Scribed by Lingju Kong; Qingkai Kong

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 205 KB
• Volume: 52
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(02)00281-x

✦ Synopsis

We consider the even order nonlinear eigenvalue problem

on a measure chain T. Results on existence and nonexistence of positive solutions are obtained for evaluated in di erent intervals. Under certain assumptions, the complete scenario for all ¿ 0 is established. Our work develops and improves many known results in the literature even for the case that T is the real number line. We also interpret our general results on measure chains to the discrete case which yields a new set of conditions for the existence and nonexistence of positive solutions of eigenvalue problems for di erence equations.