𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Superlinear systems of second-order ODE’s

✍ Scribed by Djairo G. De Figueiredo; Pedro Ubilla

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
224 KB
Volume
68
Category
Article
ISSN
0362-546X

No coin nor oath required. For personal study only.

✦ Synopsis

We discuss the existence of positive solutions of the system

where the nonlinearities f and g satisfy a superlinearity condition at both 0 and ∞. Our main result is the proof of a priori bounds for the eventual solutions. As an application, we consider the Dirichlet problem in an annulus for systems of semilinear elliptic equations with nonlinearities depending on the gradient as well. As a second application, we consider fourth-order elastic beam equations with dependence also on the derivatives u , u , u .

📜 SIMILAR VOLUMES

Systems of second-order linear ODE’s wit
Systems of second-order linear ODE’s with constant coefficients and their symmetries
✍ R. Campoamor-Stursberg 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 245 KB

Starting from the study of the symmetries of systems of 4 second-order linear ODEs with constant real coefficients, we determine the dimension and generators of the symmetry algebra for systems of \(n\) equations described by a diagonal Jordan canonical form. We further prove that some dimensions be

Forced oscillation of second order super
Forced oscillation of second order superlinear differential equations
✍ Yuan Gong Sun; James S. W. Wong 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 130 KB

## Abstract In this paper, we establish some new criteria for the oscillation of second order forced nonlinear differential equations (__r__ (__t__ )__x__ ′(__t__ ))′ + __p__ (__t__ )__x__ ′(__t__ ) + __q__ (__t__ )__f__ (__x__ (__t__ )) = __e__ (__t__ ) in both cases when __q__ (__t__ ) < 0 and __