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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Nonradial least energy solutions of the $p$-Laplace elliptic equations
Pages: 547 - 561, Issue 2, February 2018

doi:10.3934/dcds.2018024      Abstract        References        Full text (387.1K)           Related Articles

Ryuji Kajikiya - Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan (email)

1 M. Badiale and E. Serra, Multiplicity results for the supercritical Hénon equation, Adv. Nonlinear Stud., 4 (2004), 453-467.       
2 V. Barutello, S. Secchi and E. Serra, A note on the radial solutions for the supercritical Hénon equation, J. Math. Anal. Appl., 341 (2008), 720-728.       
3 J. Byeon and Z.-Q. Wang, On the Hénon equation: asymptotic profile of ground states, I, Ann. Inst. H. Poincaré Anal. Non Linéaire, 23 (2006), 803-828.       
4 J. Byeon and Z.-Q. Wang, On the Hénon equation: Asymptotic profile of ground states, II, J. Differential Equations, 216 (2005), 78-108.       
5 M. Calanchi, S. Secchi and E. Terraneo, Multiple solutions for a Hénon-like equation on the annulus, J. Differential Equations, 245 (2008), 1507-1525.       
6 D. Cao and S. Peng, The asymptotic behaviour of the ground state solutions for Hénon equation, J. Math. Anal. Appl., 278 (2003), 1-17.       
7 J.-L. Chern and C.-S. Lin, The symmetry of least-energy solutions for semilinear elliptic equations, J. Differential Equations, 187 (2003), 240-268.       
8 K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.       
9 P. Drábek and J. Milota, Methods of Nonlinear Analysis: Applications to Differential Equations, Second edition, Birkhäuser, Berlin, 2013.
10 P. Esposito, A. Pistoia and J. Wei, Concentrating solutions for the Hénon equation in $\mathbbR^2$, J. Anal. Math., 100 (2006), 249-280.       
11 N. Hirano, Existence of positive solutions for the Hénon equation involving critical Sobolev terms, J. Differential Equations, 247 (2009), 1311-1333.       
12 R. Kajikiya, Non-even least energy solutions of the Emden-Fowler equation, Proc. Amer. Math. Soc., 140 (2012), 1353-1362.       
13 R. Kajikiya, Non-radial least energy solutions of the generalized Hénon equation, J. Differential Equations, 252 (2012), 1987-2003.       
14 R. Kajikiya, Nonradial positive solutions of the $p$-Laplace Emden-Fowler equation with sign-changing weight, Mathematische Nachrichten, 289 (2016), 290-299.       
15 R. Kajikiya, Symmetric and asymmetric solutions of $p$-Laplace elliptic equations in hollow domains, To appear in Adv. Nonlinear Stud.
16 R. A. Moore and Z. Nehari, Nonoscillation theorems for a class of nonlinear differential equations, Trans. Amer. Math. Soc., 93 (1959), 30-52.       
17 R. S. Palais, The principle of symmetric criticality, Comm. Math. Phys., 69 (1979), 19-30.       
18 A. Pistoia and E. Serra, Multi-peak solutions for the Hénon equation with slightly subcritical growth, Math. Z., 256 (2007), 75-97.       
19 P. Pucci and J. Serrin, The Maximum Principle, Birkhäuser, Berlin, 2007.       
20 E. Serra, Non radial positive solutions for the Hénon equation with critical growth, Calc. Var. Partial Differential Equations, 23 (2005), 301-326.       
21 D. Smets, M. Willem and J. Su, Non-radial ground states for the Hénon equation, Commun. Contemp. Math., 4 (2002), 467-480.       
22 P. Tolksdorf, On the Dirichlet problem for quasilinear equations in domains with conical boundary points, Comm. Partial Differential Equations, 8 (1983), 773-817.       
23 J. L. Vazquez, A strong maximum principle for some quasilinear elliptic equations, Appl Math Optim, 12 (1984), 191-202.       
24 E. Zeidler, Applied Functional Analysis: Main Principles and Their Applications, Springer, New York, 1995.       

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