Nonexistence of positive solutions of nonlinear boundary value problems

• Main Author: Jeff Webb
• Format: Article
• Language: English
• Published: University of Szeged 2012-08-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: nonlocal boundary conditions; fixed point index; positive solution
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=1613

We discuss the nonexistence of positive solutions for nonlinear boundary value problems. In particular, we discuss necessary restrictions on parameters in nonlocal problems in order that (strictly) positive solutions exist. We consider cases that can be written in an equivalent integral equation form which covers a wide range of problems. In contrast to previous work, we do not use concavity arguments, instead we use positivity properties of an associated linear operator which uses ideas related to the $u_0$-positive operators of Krasnosel'skii.