On periodic elliptic equations with gradient dependence

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May 2008, 7(3): 601-615. doi: 10.3934/cpaa.2008.7.601

On periodic elliptic equations with gradient dependence

Massimiliano Berti ^1, , M. Matzeu ^2, and Enrico Valdinoci ^3,

1.	Università di Napoli Federico II, Dipartimento di Matematica e Applicazioni, Via Cintia, Monte S. Angelo, I-80126 Naples, Italy
2.	Dip. di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica - 00133 - Roma
3.	Università di Roma Tor Vergata, Dipartimento di Matematica, Via della Ricerca Scientifica, I-00133 Rome, Italy

Received March 2007 Revised November 2007 Published February 2008

Abstract
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We construct entire solutions of $\Delta u=f(x,u,\nabla u)$ which are superpositions of odd, periodic functions and linear ones, with prescribed integer or rational slope.

Keywords: Nonvariational elliptic equations, topological and analytical methods., plane-like solutions.

Mathematics Subject Classification: Primary: 35J60, 35B10; Secondary: 35B2.

Citation: Massimiliano Berti, M. Matzeu, Enrico Valdinoci. On periodic elliptic equations with gradient dependence. Communications on Pure & Applied Analysis, 2008, 7 (3) : 601-615. doi: 10.3934/cpaa.2008.7.601

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