Radial and non-radial solutions to an elliptic problem on annular domains in Riemannian manifolds with radial symmetry

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, ...

Nodal solutions of nonlinear elliptic Dirichlet problems on radial domains

Let Ω ⊂ R be a ball or an annulus and f : R → R absolutely continuous, superlinear, subcritical, and such that f(0) = 0. We prove that the least energy nodal solution of −∆u = f(u), u ∈ H 0 (Ω), is not radial. We also prove that Fučik eigenfunctions, i. e. solutions u ∈ H 0 (Ω) of −∆u = λu − μu−, with eigenvalue (λ, μ) on the first nontrivial curve of the Fučik spectrum, are not radial. A relat...

Radial Symmetry of Positive Solutions of Nonlinear Elliptic Equations

We study the radial symmetry and asymptotic behavior at x = 1 of positive solutions of u = '(jxj)u ; x 2 IR n and jxj large () where > 1 and '(r) is positive and continuous for r large. In particular we give conditions on ' which guarantee that each positive solution of () satisses u(x) u(jxj) ! 1 as jxj ! 1 where u(r) is the average of u on the sphere jxj = r.

Uniqueness and Radial Symmetry for an Inverse Elliptic Equation

whereΩ is some bounded domain inR2. In (1.1), the nonlinearity φ is unknown, and is a family of functions which are rearrangements of a prescribed function, hence problem (1.1) is named an inverse rearrangement semilinear elliptic equation. Therefore, by a solution for (1.1) we mean a pair (u,φ) which satisfies all conditions (in some sense) of (1.1). Here we are concerned with special types of...