
Existence of solutions for elliptic equations without superquadraticity condition
Yimin ZHANG, Yaotian SHEN
Front. Math. China ›› 2012, Vol. 7 ›› Issue (3) : 587-595.
Existence of solutions for elliptic equations without superquadraticity condition
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.
Mountain pass / superquadraticity condition (SQC) / Palais-Smale type condition / weakly superquadraticity condition (WSQC)
[1] |
Ambrosetti A, Rabinewitz P H. Dual variational method in critical point theory and applications. J Funct Anal, 1973, 14: 349-381
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[5] |
Huang Y S, Zhou H S. Positive solution for
CrossRef
Google scholar
|
[6] |
Jeanjean L. On the existence of bounded Palais-Smale sequences and applications to a Landesman-Lazer-type problem set on
CrossRef
Google scholar
|
[7] |
Li G B, Zhou H S. Asymptotically “linear” Dirichlet problem for the p-Laplacian. Nonlinear Anal, 2001, 43: 1043-1055
CrossRef
Google scholar
|
[8] |
Liu S B, Li S J. Infinitely 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
CrossRef
Google scholar
|
[10] |
Shen Y T, Guo X K. Discussion of nontrivial critical points of the functional
|
[11] |
Wang Z P, Zhou H S. Positive solutions for a nonhomogeneous elliptic equation on
CrossRef
Google scholar
|
/
〈 |
|
〉 |