American Institute of Mathematical Sciences

Advanced
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 and Applied Analysis, 2008, 7 (3) : 601-615. doi: 10.3934/cpaa.2008.7.601
[1]

Antonin Chambolle, Gilles Thouroude. Homogenization of interfacial energies and construction of plane-like minimizers in periodic media through a cell problem. Networks and Heterogeneous Media, 2009, 4 (1) : 127-152. doi: 10.3934/nhm.2009.4.127
[2]

Claudianor O. Alves, Djairo G. De Figueiredo. Nonvariational elliptic systems. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 289-302. doi: 10.3934/dcds.2002.8.289
[3]

Giuseppe Riey, Berardino Sciunzi. One dimensional symmetry of solutions to some anisotropic quasilinear elliptic equations in the plane. Communications on Pure and Applied Analysis, 2012, 11 (3) : 1157-1166. doi: 10.3934/cpaa.2012.11.1157
[4]

Andrea Malchiodi. Topological methods for an elliptic equation with exponential nonlinearities. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 277-294. doi: 10.3934/dcds.2008.21.277
[5]

Gabriella Tarantello. Analytical, geometrical and topological aspects of a class of mean field equations on surfaces. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 931-973. doi: 10.3934/dcds.2010.28.931
[6]

Boyan Sirakov. Notions of sublinearity and superlinearity for nonvariational elliptic systems. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 163-174. doi: 10.3934/dcds.2005.13.163
[7]

Zalman Balanov, Carlos García-Azpeitia, Wieslaw Krawcewicz. On variational and topological methods in nonlinear difference equations. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2813-2844. doi: 10.3934/cpaa.2018133
[8]

Takahiro Hashimoto. Nonexistence of positive solutions of quasilinear elliptic equations with singularity on the boundary in strip-like domains. Conference Publications, 2005, 2005 (Special) : 376-385. doi: 10.3934/proc.2005.2005.376
[9]

Takahiro Hashimoto, Mitsuharu Ôtani. Nonexistence of positive solutions for some quasilinear elliptic equations in strip-like domains. Discrete and Continuous Dynamical Systems, 1997, 3 (4) : 565-578. doi: 10.3934/dcds.1997.3.565
[10]

Gianluca Gorni, Gaetano Zampieri. Nonlocal and nonvariational extensions of Killing-type equations. Discrete and Continuous Dynamical Systems - S, 2018, 11 (4) : 675-689. doi: 10.3934/dcdss.2018042
[11]

Dominique Lecomte. Hurewicz-like tests for Borel subsets of the plane. Electronic Research Announcements, 2005, 11: 95-102.

[12]

Ruifeng Zhang, Nan Liu, Man An. Analytical solutions of Skyrme model. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 2201-2211. doi: 10.3934/dcdss.2016092
[13]

Abdon Atangana, José Francisco Gómez-Aguilar, Jordan Y. Hristov, Kolade M. Owolabi. Preface on "New trends of numerical and analytical methods". Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : i-ii. doi: 10.3934/dcdss.20203i
[14]

Jean Mawhin, James R. Ward Jr. Guiding-like functions for periodic or bounded solutions of ordinary differential equations. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 39-54. doi: 10.3934/dcds.2002.8.39
[15]

Giovany Figueiredo, Marcelo Montenegro, Matheus F. Stapenhorst. A log–exp elliptic equation in the plane. Discrete and Continuous Dynamical Systems, 2022, 42 (1) : 481-504. doi: 10.3934/dcds.2021125
[16]

Rahmat Ali Khan, Yongjin Li, Fahd Jarad. Exact analytical solutions of fractional order telegraph equations via triple Laplace transform. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2387-2397. doi: 10.3934/dcdss.2020427
[17]

Alessandro Fonda, Rafael Ortega. Positively homogeneous equations in the plane. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 475-482. doi: 10.3934/dcds.2000.6.475
[18]

Asif Yokus, Mehmet Yavuz. Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2591-2606. doi: 10.3934/dcdss.2020258
[19]

Jann-Long Chern, Sze-Guang Yang, Zhi-You Chen, Chih-Her Chen. On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3291-3304. doi: 10.3934/dcds.2020127
[20]

Huyuan Chen, Hichem Hajaiej. Classification of non-topological solutions of an elliptic equation arising from self-dual gauged Sigma model. Communications on Pure and Applied Analysis, 2021, 20 (10) : 3373-3393. doi: 10.3934/cpaa.2021109

2020 Impact Factor: 1.916

Tools

Metrics

  • PDF downloads (102)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy