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Existence of multiple non-trivial solutions for nonlinear p-Laplacian problems on ℝN

Published online by Cambridge University Press:  14 November 2011

Aiwen Wu
Aiwen Wu
Affiliation:
Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya 464, Japan
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Extract

We shall prove multiplicity of non-trivial solutions for the following p-Laplacian problems

where f(x,u) is continuous, periodic in x and has superlinear growth in u.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 4 , 1999 , pp. 855 - 883
Copyright
Copyright © Royal Society of Edinburgh 1999

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References

1Ambrosetti, A. and Zelati, V. Cotti. Multiple homoclinic orbits for a class of conservative systems. Rend. Sem. Mat. Univ. Padova. 89 (1993), 177–194.Google Scholar
2Alama, S. and Li, Y. Y.. On ‘multibump’ bound states for certain semilinear elliptic equations. Indiana Univ. Math. J. 41 (1992), 983–1026.CrossRefGoogle Scholar
3Costa, D. G. and Miyagaki, O. H.. Nontrivial solution for perturbations of the p-Laplacian on unbounded domains. J. Math. Analysis Appl. 193 (1995), 737–755.CrossRefGoogle Scholar
4Zelati, V. Coti, Ekeland, I. and Séré, E.. A varitional approach to homoclinic orbits in Hamiltonian systems. Math. Ann. 288 (1990), 133–160.CrossRefGoogle Scholar
5Zelati, V. Coti and Rabinowitz, P. H.. Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. J. Am. Math. Soc. 4 (1991), 693–727.CrossRefGoogle Scholar
6Zelati, V. Coti and Rabinowitz, P. H.. Homoclinic type solutions for a semilinear elliptic PDE on ℝN. Commun. Pure. Appl. Math. 45 (1992), 1217–1269.Google Scholar
7Zelati, V. Coti and Rabinowitz, P. H.. Multibump periodic solutions of a family of Hamiltonian systems. Topological Methods in Nonlinear Analysis: J. Juliusz Schauder Center 4 (1994), 31–57.CrossRefGoogle Scholar
8Lindgvist, P.. On the equation div(|∇u|p–2∇u) + λ|u|p–2u = 0. Proc. Am. Math. Soc. 109(1) (1990), 157–164.Google Scholar
9Jianfu, Y. and Xiping, Z.. On the existence of nontrivial solution of a quasilinear elliptic boundary value problem for unbounded domains. Acta Math. Sci. 3 (1987), 341–359.CrossRefGoogle Scholar
10Miranda, C.. Un'osservazione su un teorema di Brouwer. Boll. Unione Mat. Ital. 3 (1940), 5–7.Google Scholar
11Montecchiai, P.. Existence and multiplicity of homoclinic orbits for a class of asymptotically periodic second order Hamiltonian systems. (In the press.)Google Scholar
12Schechter, M.. A variation of the mountain pass lemma and applications. J. Lond. Math. Soc. 44 (1991), 491–502.CrossRefGoogle Scholar
13Schindler, I.. Quasilinear elliptic boundary-value problems on unbounded cylinders and a related mountain-pass lemma. Arch. Ration. Mech. Analysis 120 (1992), 363–374.CrossRefGoogle Scholar
14Séré, E.. Existence of infinitely many homoclinic orbits in Hamiltonian system. Math. Z. 209 (1992), 27–42.CrossRefGoogle Scholar
15Séré, E.. Looking for the Bernoulli shift. Ann. Inst. Henri Poincaré 10 (1993), 561–590.CrossRefGoogle Scholar