On Lane–Emden Systems with Singular Nonlinearities and Applications to MEMS

Inertial MEMS Systems and Applications

This paper provides a survey of some of the available MEMS Inertial Measurement Units (IMUs) and some of the applications that MEMS are fulfilling. Inertial MEMS have been under development for over 20 years and numerous suppliers world-wide now exist. The performance of these IMUs spans the range from consumer/automotive grade (low performance) to tactical grade (~1 deg/hour, ~1 milli g). Tact...

Degenerate elliptic equations with singular nonlinearities

The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of RN , and compactness holds below a critical dimension N #. The nonlinearity f (u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p = 2 it is crucial to...

From blow-up boundary solutions to equations with singular nonlinearities

In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of solutions and we focus on the following types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane-Emden-Fowler equations with singu...

Subelliptic equations with singular nonlinearities on the Heisenberg group

Iterative Solution of Singular Systems with Applications