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We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small energy/charge ratio, appropriately defined.
For a general class of autonomous quasi-linear elliptic equations on R^n we prove the existence of a least energy solution and show that all least energy solutions do not change sign and are radially symmetric up to a translation in R^n.
Let $Omega subset mathbb{R}^N$ be a bounded domain and $delta(x)$ be the distance of a point $xin Omega$ to the boundary. We study the positive solutions of the problem $Delta u +frac{mu}{delta(x)^2}u=u^p$ in $Omega$, where $p>0, ,p e 1$ and $mu in m
Using the sub-supersolution method we study the existence of positive solutions for the anisotropic problem begin{equation} -sum_{i=1}^Nfrac{partial}{partial x_i}left( left|frac{partial u}{partial x_i}right|^{p_i-2}frac{partial u}{partial x_i}right)=
This paper deals with existence and regularity of positive solutions of singular elliptic problems on a smooth bounded domain with Dirichlet boundary conditions involving the $Phi$-Laplacian operator. The proof of existence is based on a variant of t
The paper aims at constructing two different solutions to an elliptic system $$ u cdot abla u + (-Delta)^m u = lambda F $$ defined on the two dimensional torus. It can be viewed as an elliptic regularization of the stationary Burgers 2D system