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

Aleksandra Orpel

doi:10.3934/dcdsb.2014.19.2631

Article Contents

2014, Volume 19, Issue 8: 2631-2639. Doi: 10.3934/dcdsb.2014.19.2631

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

Aleksandra Orpel^1,

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

Received: September 30, 2013

Revised: March 31, 2014

Published: September 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B40, 35J15, 35J60; Secondary: 34B15, 47H10.

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