Solutions to semilinear elliptic problems with combined nonlinearities

Journal of Differential Equations

Volumn 185, Issue 1, 2002, Pages 200-224

  Li, Shujie ^a   Wu, Shaoping ^b   Zhou, Huan Song ^c  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

^b ZHEJIANG UNIVERSITY   (China)

^c Wuhan National Laboratory for Optoelectronics   (China)

Author keywords

Asymptotically linear; Elliptic problem; Mountain pass theorem; Sublinear; Superlinear

Indexed keywords

EID: 0037058011     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4167     Document Type: Article

References (31)

1. N with critical exponents, Electron. J. Differential Equations 1997 (1997), 1-10.
2. N involving critical exponents, Nonlinear Anal. 34 (1998), 593-615.
3. A. Ambrosetti, H. Brezis, and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), 519-543.
4. A. Ambrosertt and P. Rabinowitz, Dual variational methods in critical points theory and applications, J. Funct. Anal. 14 (1973), 349-381.
5. P. Bartolo, V. Benci, and D. Fortunato, Abstract critical theorems and applications to some nonlinear problems with "strong" resonance at infinity, Nonlinear Anal. 7 (1983), 981-1012.
6. H. Berestycki and P. L. Lions, Nonlinear scalar field equations, (I), Arch. Rational Mech. Anal. 82 (1983), 313-376.
7. H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477.
8. H. Brezis and H. Oswald, Remarks on sublinear elliptic equations, Nonlinear Anal. 10 (1986), 55-64.
9. D. M. Cao and H. S. Zhou, On the existence of multiple solutions of inhomogeneous elliptic equations involving critical Sobolev exponents, Z. Angew. Math. Phys. 47 (1996), 89-97.
10. D. G. Costa and C. A. Magalhães, Variational elliptic problems which are nonquadratic at infinity, Nonlinear Anal. 23 (1994), 1401-1412.
11. D. G. Costa and O. H. Miyagaki, Nontrivial solutions for perturbations of the p-Laplacian on unbounded domains, J. Math. Anal. Appl. 193 (1995), 737-755.
12. D. G. Costa and E. A. Silva, On a class of resonant problems at higher eigenvalues, Differential Integral Equations 8 (1995), 663-671.
13. I. Ekeland, Nonconvex minimization problems, Bull Amer. Math. Soc. 1 (1979), 443-473.
14. I. Ekeland, "Convexity Methods in Hamiltonian Mechanics," Springer-Verlag, Berlin, 1990.
15. D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," 2nd ed., Springer-Verlag, Berlin/Heidelberg, 1983.
16. N involving subcritical exponents, Nonlinear Anal. 32 (1998), 41-51.
17. N, Electron. J. Differential Equations 1997 (1997), 1-15.
18. B. do O. Joao Marcos, Existence of solutions for quasilinear elliptic equations, J. Math. Anal. Appl. 207 (1997), 104-126.
19. L. Jeanjean, On the existence of bounded Palais-Smale sequences and application to a Landesmann-Lazer type problem, Proc. Roy. Soc. Edinburgh, Sect. A 129A (1999), 787-809.
20. G. B. Li and H. S. Zhou, The existence of a weak solution of inhomogeneous quasilinear elliptic equation with critical growth conditions, Acta Math. Sinica (N.S.), 11 (1995), 146-155.
21. J. Mawhin, J. R. Ward, and M. Wiellm, Variational methods and semilinear elliptic equations, Arch. Rational Mech. Anal. 113 (1991), 65-96.
22. K. Perera, Multiplicity results for some elliptic problems with concave nonlinearities, J. Differential Equations 140 (1997), 133-141.
23. M. Schechter, A variation of the Mountain Pass lemma and applications, J. London Math. Soc. 44 (1991), 491-502.
24. M. Schechter, Superlinear elliptic boundary value problems, Manuscripta Math. 86 (1995), 253-265.
25. C. A. Stuart and H. S. Zhou, A variational problem related to self-trapping of an electromagnetic field, Math. Methods Appl. Sci. 19 (1996), 1397-1407.
26. N, Comm. Partial Differential Equations 24 (1999) 1731 1758.
27. G. Tarantello, On nonhomogeneous elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincare Anal. Non Linéaire 9 (1992), 243-261.
28. Z. Q. Wang, Nonlinear boundary value problems with concave nonlinearities near the origin, Nonlinear Differential Equations Appl. 8 (2001), 15-33.
29. S. P. Wu and H. T. Yang, A class of resonant elliptic problems with sublinear nonlinearity at origin and infinity, preprint.
30. H. S. Zhou, Positive solution for a semilinear elliptic equation which is almost linear at infinity, Z. Angew Math. Phys. 49 (1998), 896-906.
31. X. P. Zhu, A perturbation result on positive entire solutions of a semilinear elliptic equations, J. Differential Equations 92 (1991), 163-178.