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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

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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