Existence of solutions for elliptic equations without superquadraticity condition

Yimin Zhang , Yaotian Shen

Front. Math. China ›› 2012, Vol. 7 ›› Issue (3) : 587 -595.

PDF (132KB)
Front. Math. China ›› 2012, Vol. 7 ›› Issue (3) : 587 -595. DOI: 10.1007/s11464-012-0211-8
Research Article
RESEARCH ARTICLE

Existence of solutions for elliptic equations without superquadraticity condition

Author information +
History +
PDF (132KB)

Abstract

By weakening or dropping the superquadraticity condition (SQC), the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotical linearities as well as the superlinear nonlinearities.

Keywords

Mountain pass / superquadraticity condition (SQC) / Palais-Smale type condition / weakly superquadraticity condition (WSQC)

Cite this article

Download citation ▾
Yimin Zhang, Yaotian Shen. Existence of solutions for elliptic equations without superquadraticity condition. Front. Math. China, 2012, 7(3): 587-595 DOI:10.1007/s11464-012-0211-8

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Ambrosetti A., Rabinewitz P. H. Dual variational method in critical point theory and applications. J Funct Anal, 1973, 14: 349-381

[2]

Cerami G. Un criterio de esistenza per i punti critici su varietà illimitate. Rc Ist Lomb Sci Lett, 1978, 112: 332-336

[3]

Chen Z. H., Shen Y. T., Yao Y. X. Some existence results of solutions for p-Laplacian. Acta Math Sci, 2003, 23B: 487-496

[4]

Costa D. G., Magalhães C. A. Variational elliptic problems which are nonquadratic at infinity. Nonlinear Anal, 1994, 23: 1401-1412

[5]

Huang Y. S., Zhou H. S. Positive solution for −Δpu = f(x, u) with f(x, u) growing as up−1 at infinity. Appl Math Lett, 2004, 17: 881-887

[6]

Jeanjean L. On the existence of bounded Palais-Smale sequences and applications to a Landesman-Lazer-type problem set on ℝN. Proc Roy Soc Edinburgh, 1999, 129A: 787-809

[7]

Li G. B., Zhou H. S. Asymptotically “linear” Dirichlet problem for the p-Laplacian. Nonlinear Anal, 2001, 43: 1043-1055

[8]

Liu S. B., Li S. J. I. nfinitely many solutions for a superlinear elliptic equation. Acta Math Sinica, 2003, 46(4): 625-630

[9]

Schechter M., Zou W. M. Superlinear problems. Pacific J Math, 2004, 214: 145-160

[10]

Shen Y. T., Guo X. K. Discussion of nontrivial critical points of the functional ΣΩF(x, u, Du)dx. Acta Math Sci, 1987, 10: 249-258

[11]

Wang Z. P., Zhou H. S. Positive solutions for a nonhomogeneous elliptic equation on ℝN without (AR) condition. J Math Anal Appl, 2009, 353: 470-479

AI Summary AI Mindmap
PDF (132KB)

806

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/