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 & 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 & 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 & Continuous Dynamical Systems - A, 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 & 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 & Continuous Dynamical Systems - A, 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 & Continuous Dynamical Systems - A, 2010, 28 (3) : 931-973. doi: 10.3934/dcds.2010.28.931
[6]

Zalman Balanov, Carlos García-Azpeitia, Wieslaw Krawcewicz. On variational and topological methods in nonlinear difference equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2813-2844. doi: 10.3934/cpaa.2018133
[7]

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
[8]

Takahiro Hashimoto, Mitsuharu Ôtani. Nonexistence of positive solutions for some quasilinear elliptic equations in strip-like domains. Discrete & Continuous Dynamical Systems - A, 1997, 3 (4) : 565-578. doi: 10.3934/dcds.1997.3.565
[9]

Boyan Sirakov. Notions of sublinearity and superlinearity for nonvariational elliptic systems. Discrete & Continuous Dynamical Systems - A, 2005, 13 (1) : 163-174. doi: 10.3934/dcds.2005.13.163
[10]

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

Ruifeng Zhang, Nan Liu, Man An. Analytical solutions of Skyrme model. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 2201-2211. doi: 10.3934/dcdss.2016092
[12]

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

[13]

Jean Mawhin, James R. Ward Jr. Guiding-like functions for periodic or bounded solutions of ordinary differential equations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (1) : 39-54. doi: 10.3934/dcds.2002.8.39
[14]

G. Machado, L. Trabucho. Analytical and numerical solutions for a class of optimization problems in elasticity. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 1013-1032. doi: 10.3934/dcdsb.2004.4.1013
[15]

Alessandro Fonda, Rafael Ortega. Positively homogeneous equations in the plane. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 475-482. doi: 10.3934/dcds.2000.6.475
[16]

Wansheng Wang, Chengjian Zhang. Analytical and numerical dissipativity for nonlinear generalized pantograph equations. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 1245-1260. doi: 10.3934/dcds.2011.29.1245
[17]

Marian Gidea, Rafael De La Llave. Topological methods in the instability problem of Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2006, 14 (2) : 295-328. doi: 10.3934/dcds.2006.14.295
[18]

Víctor Jiménez López, Gabriel Soler López. A topological characterization of ω-limit sets for continuous flows on the projective plane. Conference Publications, 2001, 2001 (Special) : 254-258. doi: 10.3934/proc.2001.2001.254
[19]

Anton Trushechkin. Microscopic and soliton-like solutions of the Boltzmann--Enskog and generalized Enskog equations for elastic and inelastic hard spheres. Kinetic & Related Models, 2014, 7 (4) : 755-778. doi: 10.3934/krm.2014.7.755
[20]

J. Ángel Cid, Pedro J. Torres. On the existence and stability of periodic solutions for pendulum-like equations with friction and $\phi$-Laplacian. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 141-152. doi: 10.3934/dcds.2013.33.141

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences