The existence of a positive solution to asymptotically linear scalar field equations

Royal Society of Edinburgh - Proceedings A

Volumn 130, Issue 1, 2000, Pages 81-105

  Li, G ^a   Zhou, H S ^a  

^a Wuhan National Laboratory for Optoelectronics   (China)

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EID: 22844456350     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500000068     Document Type: Article

References (20)

1. A. Ambrosetti and R. Rabinowitz. Dual variational methods in critical points theory and applications. J. Funct. Analysis 14 (1973), 349-381.
2. H. Berestycki and P. L. Lions. Nonlinear scalar field equations (I). Arch. Ration. Mech. Analysis 82 (1983), 313-376.
3. H. Brezis and L. Nirenberg. Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents. Commun. Pure Appl. Math. 36 (1983), 437-477.
4. K. C. Chang. Critical point theory and its applications (Shanghai Scientific and Technical Press, 1986) (in Chinese).
5. D. G. Costa and C. A. Magalhães. Variational elliptic problems which are nonquadratic at infinity. Nonlin. Analysis TMA 23 (1994), 1401-1412.
6. D. G. Costa and O. H. Miyagaki. Nontrivial solutions for perturbations of the p-Laplacian on unbounded domains. J. Math. Analysis Applic. 193 (1995), 737-755.
7. W. Y. Ding and W. M. Ni. On the existence of positive entire solutions of a semilinear elliptic equation. Arch. Ration. Mech. Analysis 91 (1986), 283-308.
8. L. Jeanjean. On the existence of bounded Palais-Smale sequences and application to a Landesmann-Lazer type problem. Proc. R. Soc. Edinb. A 129 (1999), 787-809.
9. Y. Y. Li. Nonautonomous nonlinear scalar field equations. Indiana Univ. Math. J. 39 (1990), 283-301.
10. P. L. Lions. The concentration-compactness principle in the calculus of variations. The local compact case. Part 1. Ann. Inst. H. Poincaré Analyse Non Lineare 1 (1984), 109-145.
11. P. L. Lions. The concentration-compactness principle in the calculus of variations. The local compact case. Part 2. Ann. Inst. H. Poincaré Analyse Non Linéare 1 (1984), 223-283.
12. M. Schechter. Superlinear elliptic boundary value problems. Manuscripta Math. 86 (1995), 253-265.
13. W. A. Strauss. Existence of solitary waves in higher dimensions. Commun. Math. Phys. 55 (1977), 149-162.
14. C. A. Stuart. Bifurcation for Dirichlet problems without eigenvalues. Proc. Lond. Math. Soc. 45 (1982), 149-162.
15. C. A. Stuart. Self-trapping of an electromagnetic field and bifurcation from the essential spectrum. Arch. Ration. Mech. Analysis 113 (1991), 65-96.
16. C. A. Stuart. Magnetic field wave equations for TM-modes in nonlinear optical waveguides. In Reaction diffusion systems (ed. E. Caristi and G. Mitidieri), pp. 377-400 (Marcel Dekker, 1997).
17. C. A. Stuart and H. S. Zhou. A variational problem related to self-trpping of an electromagnetic field. Math. Methods Applic. Sci. 19 (1996), 1397-1407.
18. N. Commun. PDE 24 (1999), 1731-1758.
19. J. F. Yang and X. P. Zhu. On the existence of nontrivial solution of a quasilinear elliptic boundary value problem for unbounded domains. I. Positive mass case. Acta Math. Sci. 7 (1987), 341-359.
20. H. S. Zhou. Positive solution for a semilinear elliptic equation which is almost linear at infinity. Z. Angew. Math. Phys. (ZAMP) 49 (1988), 896-906.