Positive solution for a semilinear elliptic equation which is almost linear at infinity

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 49, Issue 6, 1998, Pages 896-906

  Zhou, Huan Song ^a  

^a Wuhan National Laboratory for Optoelectronics   (China)

Author keywords

Mountain pass; Positive solution; Semilinear elliptic equation

Indexed keywords

EID: 0032281604     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000330050128     Document Type: Article

References (21)

1. A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical points theory and applications, J. Fund. Anal. 14 (1973), 349-381.
2. P. Bartolo, V. Benci and D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with "strong" resonance at infinity, Nonlin. Anal. TMA, 7 (1983)9, 981-1012.
3. H. Berestycki and P.L. Lions, Nonlinear scalar field equations, (I), Arc. Rat. Mech. Anal., 82 (1983), 313-376.
4. G. Bianchi, J. Chabrowski and A. Szulkin, On symmetric solutions of an elliptic equation with a nonlinearity involving critical Sobolev exponent, Nonli. Anal. TMA, 25 (1995), 41-59.
5. H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477.
6. H. Brezis and L. Oswald, Remarks on sublinear elliptic equations, Nonli. Anal. TMA, 10 (1986), 55-64.
7. D.G. Costa and C.A. Magalhāes, Variational elliptic problems which are nonquadratic at infinity, Nonli. Anal. TMA, 23 (1994), 1401-1412.
8. W.Y. Ding and W.M. Ni, On the existence of positive entire solutions of a semilinear elliptic equation, Arch. Rat. Mech. Anal., 91 (1986), 283-308.
9. D.G. de Figueiredo, Positive solutions for some class of semilinear elliptic problems, Proc. of Symposia in pure Math., 45 (1986), part 1, 371-379.
10. O. John, C.A. Stuart, Guidance properties of a cylindrical defocusing waveguide, Comm. Math. Univ. Carolinae, 35 (1994), 653-673.
11. Y.Y. Li, Nonautonomous nonlinear scalar field equations, India. Uni. Math. J., 39 (1990), 283-301.
12. P.L. Lions, The concentration-compactness principle in the calculus of variations, The local compact case, part 2, Ann. I. H. P. Anal. Nonli., 1 (1984), 223-283.
13. J. Mawhin, J.R. Ward and M. Willem, Variational methods and semilinear elliptic equations, Arch. Rat. Mech. Anal., 95 (1986), 269-277.
14. W. Rother, Bifurcation for a semilinear elliptic equation on RN with radially symmetric coefficients, Manuscripta Math., 65 (1989), 413-426.
15. H.-J. Ruppen, Multiple TE-Modes for cylindrical self-focusing waveguides, Preprint.
16. M. Schechter, Superlinear elliptic boundary value problems, Manu-scripta Math., 86 (1995), 253-265.
17. W.A. Strauss, Existence of solitary waves in higher dimensions, Comm. in Math. Phys., 55 (1977), 149-162.
18. C.A. Stuart, Self-trapping of an electromagnetic field and bifurcation from the essential spectrum, Arch. Rat. Mech. Anal., 113 (1991), 65-96.
19. C.A. Stuart, Guidance properties of nonlinear planar waveguides, Arch. Rat. Mech. Anal., 125 (1993), 145-200.
20. C.A. Stuart, Bifurcation for Dirichlet problems without eigenvalues, Proc. London Math. Soc. , 45 (1982), 149-162.
21. C.A. Stuart and H.S. Zhou, A variational problem related to self-trapping of an electromagnetic field, Math. Methods in Appli. Sci., 19 (1996), 1397-1407.