Bubble towers for supercritical semilinear elliptic equations

Numerical Simulation of Separation Bubble on Elliptic Cylinders Using Three-equation k-? Turbulence Model

Occurrence of laminar separation bubbles on solid walls of an elliptic cylinder has been simulated using a recently developed transitional model for boundary layer flows. Computational method is based on the solution of the Reynolds averaged Navier-Stokes (RANS) equations and the eddy-viscosity concept. Transitional model tries to simulate streamwise fluctuations, induced by freestream turbulen...

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Non-existence and uniqueness results for supercritical semilinear elliptic equations

Non-existence and uniqueness results are proved for several local and non-local supercritical bifurcation problems involving a semilinear elliptic equation depending on a parameter. The domain is star-shaped and such that a Poincaré inequality holds but no other symmetry assumption is required. Uniqueness holds when the bifurcation parameter is in a certain range. Our approach can be seen, in s...

Sign-changing Bubble Towers for Asymptotically Critical Elliptic Equations on Riemannian Manifolds

Given a smooth compact Riemannian n–manifold (M, g), we consider the equation ∆gu+ hu = |u| ∗−2−ε u, where h is a C–function on M , the exponent 2∗ := 2n/ (n− 2) is the critical Sobolev exponent, and ε is a small positive real parameter such that ε→ 0. We prove the existence of blowing-up families of sign-changing solutions which develop bubble towers at some point where the function h is great...

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.