Positive radial solutions and non-radial bifurcation for semilinear elliptic 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, ...

Uniqueness of Radial Solutions of Semilinear Elliptic Equations

E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one nite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coeecients. One particular example covered is u + u p u = 0, with p > 1. The key ingredients of the method are energy function...

Regularity of Radial Extremal Solutions of Semilinear Elliptic Equations

with φ a C∞ function with compact support in Ω. Note that Qu corresponds to the second variation of the energy associated to (1). We say that u is semi-stable if Qu(φ) ≥ 0 for all such φ. If u is bounded, this is equivalent to the nonnegativeness of the first eigenvalue in Ω of the linearized problem −∆− g′(u) of (1) at u. In [CC2] we establish sharp pointwise, L, and W k,q estimates for semi-s...

Three positive radial solutions for elliptic equations in a ball

In this work we deal with a class of second-order elliptic problems of the form − u = λk(|x |) f (u) in Ω , with non-homogeneous boundary condition u = a on ∂Ω where Ω is the ball of radius R0 centered at origin, λ, a are positive parameters, f ∈ C([0,+∞), [0,+∞)) is an increasing function and k ∈ C([0, R0], [0,+∞)) is not identically zero on any subinterval of [0, R0]. We obtain via a fixed po...