Positive Radial Solutions for Semilinear Biharmonic Equations in Annular Domains

Multiple Positive Radial Solutions for Quasilinear Equations in Annular Domains

Multiplicity and Symmetry Breaking for Positive Radial Solutions of Semilinear Elliptic Equations Modelling Mems on Annular Domains

The use of electrostatic forces to provide actuation is a method of central importance in microelectromechanical system (MEMS) and in nanoelectromechanical systems (NEMS). Here, we study the electrostatic deflection of an annular elastic membrane. We investigate the exact number of positive radial solutions and non-radially symmetric bifurcation for the model −∆u = λ (1− u)2 in Ω, u = 0 on ∂Ω, ...

Radial entire solutions for supercritical biharmonic equations ∗

We prove existence and uniqueness (up to rescaling) of positive radial entire solutions of supercritical semilinear biharmonic equations. The proof is performed with a shooting method which uses the value of the second derivative at the origin as a parameter. This method also enables us to find finite time blow up solutions. Finally, we study the convergence at infinity of regular solutions tow...

Computation of radial solutions of semilinear equations

We express radial solutions of semilinear elliptic equations on Rn as convergent power series in r, and then use Pade approximants to compute both ground state solutions, and solutions to Dirichlet problem. Using a similar approach we have discovered existence of singular solutions for a class of subcritical problems. We prove convergence of the power series by modifying the classical method of...

Exact solutions of semilinear radial wave equations in n dimensions

Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method is based on the introduction of groupinvariant jet space variables associated with the point symmetry group admitted for the wave equation and is applicable more generally to any nonlinear PDEs. It is shown to yield not only group-invariant solutions as derived by standard symmetr...