On periodic elliptic equations with gradient dependence

Massimiliano Berti; M. Matzeu; Enrico Valdinoci

doi:10.3934/cpaa.2008.7.601

Article Contents

2008, Volume 7, Issue 3: 601-615. Doi: 10.3934/cpaa.2008.7.601

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On periodic elliptic equations with gradient dependence

1.
Università di Napoli Federico II, Dipartimento di Matematica e Applicazioni, Via Cintia, Monte S. Angelo, I-80126 Naples
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

Received: February 28, 2007

Revised: October 31, 2007

Published: April 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J60, 35B10; Secondary: 35B27.

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