American Institute of Mathematical Sciences

October  2014, 19(8): 2631-2639. doi: 10.3934/dcdsb.2014.19.2631

A note on the existence and properties of evanescent solutions for nonlinear elliptic problems

 1 Faculty of Mathematics and Computer Science, University of Lodz, S. Banacha 22, 90-238 Lodz, Poland

Received  October 2013 Revised  April 2014 Published  August 2014

Basing ourselves on the subsolution and supersolution method we investigate the existence and properties of solutions of the following class of elliptic differential equations $div(a(||x||)\nabla u(x)) + f(x,u(x)) + g(||x||)k(x\cdot\nabla u(x)) = 0,$ $x\in\mathbb{R}^{n},||x||>R.$ Our main result concernes the behavior of solution at infinity.
Citation: Aleksandra Orpel. A note on the existence and properties of evanescent solutions for nonlinear elliptic problems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2631-2639. doi: 10.3934/dcdsb.2014.19.2631
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