THREE NONTRIVIAL NONNEGATIVE SOLUTIONS FOR SOME CRITICAL p-LAPLACIAN SYSTEMS WITH LOWER-ORDER NEGATIVE PERTURBATIONS |
Chu, Chang-Mu
(College of Science Guizhou Minzu University)
Lei, Chun-Yu (College of Science Guizhou Minzu University) Sun, Jiao-Jiao (College of Science Guizhou Minzu University) Suo, Hong-Min (College of Science Guizhou Minzu University) |
1 | A. Ambrosetti, H. Brezis, and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), no. 2, 519-543. DOI |
2 | A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 347-381. |
3 | P. Amster, P. De Napoli, and M. C. Mariani, Cristina existence of solutions for elliptic systems with critical Sobolev exponent, Electron J. Differential Equations 2002 (2002), no. 49, 13 pp. |
4 | G. Anello, Multiple nonnegative solutions for an elliptic boundary value problem involving combined nonlinearities, Math. Comput. Modelling 52 (2010), no. 1-2, 400-408. DOI |
5 | G. Anello, Multiplicity and asymptotic behavior of nonnegative solutions for elliptic problems involving nonlinearities indefinite in sign, Nonlinear Anal. 75 (2012), no. 8, 3618-3628. DOI |
6 | H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functional, Proc. Amer. Math. Soc. 88 (1983), no. 3, 486-490. DOI |
7 | C. M. Chu and C. L. Tang, Existence and multiplicity of positive solutions for semilinear elliptic systems with Sobolev critical exponents, Nonlinear Anal. 71 (2009), no. 11, 5118-5130. DOI |
8 | I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324-353. DOI |
9 | Q. Y. Dai and L. H. Peng, Necessary and sufficient conditions for the existence of nonnegative solutions of inhomogeneous p-Laplace equation, Acta Math. Sci. Ser. B Engl. Ed. 27 (2007), no. 1, 34-56. |
10 | H. Egnell, Existence and nonexistence results for m-Laplace equations involving critical Sobolev exponents, Arch. Rational Mech. Anal. 104 (1988), no. 1, 57-77. DOI |
11 | D. G. de Figueiredo, J. P. Gossez, and P. Ubilla, Local "superlinearity" and "sublinearity" for the p-Laplacian, J. Funct. Anal. 3 (2009), no. 3, 721-752. |
12 | J. Garcia Azorero and I. P. Alonso, Some results about the existence of a second positive solution in a quasilinear critical problem, Indiana Univ. Math. J. 43 (1994), no. 3, 941-957. DOI |
13 | J. Garcia Azorero, I. P. Alonso, and J. J. Manfredi, Sobolev versus Holder local minimizers and global multiplicity for some quasilinear elliptic equations, Commun. Contemp. Math. 2 (2000), no. 3, 385-404. DOI |
14 | T. X. Li and T. F. Wu, Multiple positive solutions for a Dirichlet problem involving critical Sobolev exponent, J. Math. Anal. Appl. 369 (2010), no. 1, 245-257. DOI |
15 | P. G. Han, Multiple positive solutions of nonhomogeneous elliptic systems involving critical Sobolev exponents, Nonlinear Anal. 64 (2006), no. 4, 869-886. DOI |
16 | T. S. Hsu, Multiplicity results for p-Laplacian with critical nonlinearity of concaveconvex type and sign-changing weight functions, Abstr. Appl. Anal. 2009 (2009), Art. ID 652109, 24 pp. |
17 | 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. DOI |
18 | G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pura Appl. (4) 110 (1976), 353-372. DOI |
19 | D. C. de Morais Filho and M. A. S. Souto, Systems of p-Laplacean equations involving homogeneous nonlinearities with critical Sobolev exponent degrees, Comm. Partial Differential Equations 24 (1999), no. 7-8, 1537-1553. DOI |
20 | Y. Shen and J. H. Zhang, Multiplicity of positive solutions for semilinear p-Laplacian system with Sobolev critical exponent, Nonlinear Anal. 74 (2011), 1019-1030. DOI |
21 | T. F. Wu, On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function, Commun. Pure Appl. Anal. 7 (2008), no. 2, 383-405. DOI |