JOURNAL BROWSE
Search
Advanced SearchSearch Tips
MULTIPLICITY OF SOLUTIONS FOR BIHARMONIC ELLIPTIC SYSTEMS INVOLVING CRITICAL NONLINEARITY
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
MULTIPLICITY OF SOLUTIONS FOR BIHARMONIC ELLIPTIC SYSTEMS INVOLVING CRITICAL NONLINEARITY
Lu, Dengfeng; Xiao, Jianhai;
  PDF(new window)
 Abstract
In this paper, we consider the biharmonic elliptic systems of the form , where is a bounded domain with smooth boundary , is the biharmonic operator, , < , denotes the critical Sobolev exponent, is homogeneous function of degree . By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on and .
 Keywords
biharmonic elliptic system;critical Sobolev exponent;variational method;multiple solutions;
 Language
English
 Cited by
1.
ON A CLASSIFICATION OF WARPED PRODUCT SPACES WITH GRADIENT RICCI SOLITONS, Korean Journal of Mathematics, 2016, 24, 4, 627  crossref(new windwow)
 References
1.
C. O. Alves and Y. H. Ding, Multiplicity of positive solutions to a p-Laplacian equation involving critical nonlinearity, J. Math. Anal. Appl. 279 (2003), no. 2, 508-521. crossref(new window)

2.
T. Bartsch and Y. Guo, Existence and nonexistence results for critical growth polyhar- monic elliptic systems, J. Differential Equations 220 (2006), no. 2, 531-543. crossref(new window)

3.
F. Bernis, J. Garcia-Azorero, and I. Peral, Existence and multiplicity of nontrivial so- lutions in semilinear critical problems of fourth order, Adv. Differential Equations 1 (1996), no. 2, 219-240.

4.
H. Brezis and E. Lieb, A relation between pointwise convergence of functions and con- vergence of functionals, Proc. Amer. Math. Soc. 88 (1983), no. 3, 486-490. crossref(new window)

5.
J. Chabrowski and J. Marcos do O, On some fourth-order semilinear elliptic problems in RN, Nonlinear Anal. 49 (2002), no. 6, 861-884. crossref(new window)

6.
L. Ding and S. W. Xiao, Multiple positive solutions for a critical quasilinear elliptic system, Nonlinear Anal. 72 (2010), no. 5, 2592-2607. crossref(new window)

7.
D. E. Edmunds, D. Fortunato, and E. Jannelli, Critical exponents, critical dimensions and the biharmonic operator, Arch. Rational Mech. Anal. 112 (1990), no. 3, 269-289. crossref(new window)

8.
D. C. de Morais Filho and M. A. S. Souto, Systems of p-Laplacian equations involv- ing homogeneous nonlinearities with critical Sobolev exponent degrees, Comm. Partial Differential Equations 24 (1999), no. 7-8, 1537-1553. crossref(new window)

9.
F. Gazzola, H.C. Grunau, and M. Squassina, Existence and nonexistence results for critical growth biharmonic elliptic equations, Calc. Var. Partial Differential Equations 18 (2003), no. 2, 117-143. crossref(new window)

10.
Y. X. Ge, J. C. Wei, and F. Zhou, A critical elliptic problem for polyharmonic operators, J. Funct. Anal. 260 (2011), no. 8, 2247-2282. crossref(new window)

11.
H. Grunau, Positive solutions to semilinear polyharmonic Dirichlet problems involving critical Sobolev exponents, Calc. Var. Partial Differential Equations 3 (1995), no. 2, 243-252. crossref(new window)

12.
P. G. Han, The effect of the domain topology on the number of positive solutions of an elliptic systems involving critical Sobolev exponents, Houston J. Math. 32 (2006), no. 4, 1241-1257.

13.
T. S. Hsu and H. L. Lin, Multiple positive solutions for a critical elliptic system with concave-convex nonlinearities, Proc. Roy. Soc. Edinburgh Sect. A 139 (2009), no. 6, 1163-1177. crossref(new window)

14.
D. S. Kang and S. J. Peng, Existence and asymptotic properties of solutions to elliptic systems involving multiple critical exponents, Sci.China Math. 54 (2011), no. 2, 243-256. crossref(new window)

15.
D. F. Lu, Multiple solutions for a class of biharmonic elliptic systems with Sobolev critical exponent, Nonlinear Anal. 74 (2011), no. 17, 6371-6382. crossref(new window)

16.
D. F. Lu and J. H. Xiao, Multiple solutions for weighted nonlinear elliptic system in-volving critical exponents, Math. Comput. Modelling 55 (2012), no. 3-4, 816-827. crossref(new window)

17.
M. Montenegro, On nontrivial solutions of critical polyharmonic elliptic systems, J. Differential Equations 247 (2009), no. 3, 906-916. crossref(new window)

18.
E. S. Noussair, C. A. Swanson, and J. Yang, Critical semilinear biharmonic equations in $R^N$, Proc. Roy. Soc. Edinburgh Sect. A 121 (1992), no. 1-2, 139-148. crossref(new window)

19.
O. Rey, A multiplicity results for a variational problem with lack of compactness, Nonlinear Anal. 13 (10) (1989), no. 10, 1241-1249. crossref(new window)

20.
Y. Shen and J. H. Zhang, Multiplicity of positive solutions for a semilinear p-Laplacian system with Sobolev critical exponent, Nonlinear Anal. 74 (2011), no. 4, 1019-1030. crossref(new window)

21.
Y. J. Wang and Y. T. Shen, Multiple and sign-changing solutions for a class of semi-linear biharmonic equation, J. Differential Equations 246 (2009), no. 8, 3109-3125. crossref(new window)

22.
M. Willem, Minimax Theorems, Birkhauser, Boston, 1996.

23.
Y. J. Zhang, Positive solutions of semilinear biharmonic equations with critical Sobolev exponents, Nonlinear Anal. 75 (2012), no. 1, 55-67. crossref(new window)