We obtain a non-existence result for a class of quasi-linear eigenvalue problems when a parameter is small. By using Pohozaev identity and some comparison arguments, non-existence theorems are established for quasi-linear eigenvalue problems under supercritical growth condition.

The nonlinear eigenvalue problem for p-Laplacian $$\left\{\begin{array}{c}-{div\left(a\left(x\right)\right|\nabla u|}^{p-2}{\nabla u)=\lambda g\left(x\right)|u|}^{p-2}u\text{in}{ℝ}^N,u>0\text{in}{ℝ}^N,\underset{\left|x\right|\to \infty }{lim}u\left(x\right)=0,\hfill \end{array}\right.$$ is considered. We assume that $1<p<N$ and that $g$ is indefinite weight function. The existence and $C^{1,\alpha }$-regularity of the weak solution is proved.

The non-local Gel’fand problem, $\Delta v+\lambda e^v/{\int }_{\Omega }{e}^{v}dx=0$ with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.

In this article, we provide a priorierror estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the...

In this article, we provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the...