JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GROUND STATE SOLUTIONS OF NON-RESONANT COOPERATIVE ELLIPTIC SYSTEMS WITH SUPERLINEAR TERMS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GROUND STATE SOLUTIONS OF NON-RESONANT COOPERATIVE ELLIPTIC SYSTEMS WITH SUPERLINEAR TERMS
Chen, Guanwei;
  PDF(new window)
 Abstract
In this paper, we study the existence of ground state solutions for a class of non-resonant cooperative elliptic systems by a variant weak linking theorem. Here the classical Ambrosetti-Rabinowitz superquadratic condition is replaced by a general super quadratic condition.
 Keywords
non-resonant cooperative elliptic systems;ground state solutions;superlinear;variant weak linking theorem;
 Language
English
 Cited by
1.
Multiple solutions of superlinear cooperative elliptic systems at resonant, Nonlinear Analysis: Real World Applications, 2017, 34, 264  crossref(new windwow)
2.
Infinitely Many Nontrivial Solutions of Resonant Cooperative Elliptic Systems with Superlinear Terms, Abstract and Applied Analysis, 2014, 2014, 1  crossref(new windwow)
 References
1.
G. Chen and S. Ma, Infinitely many solutions for resonant cooperative elliptic systems with sublinear or superlinear terms, Calc. Var. Partial Differential Equations 49 (2014), no. 1-2, 271-286. crossref(new window)

2.
G. Chen and S. Ma, Asymptotically or super linear cooperative elliptic systems in the whole space, Sci. China Math. 56 (2013), no. 6, 1181-1194. crossref(new window)

3.
D. G. Costa and C. A. Magalhaes, A variational approach to subquadratic perturbations of elliptic systems, J. Differential Equations 111 (1994), no. 1, 103-122. crossref(new window)

4.
D. G. Costa and C. A. Magalhaes, A unified approach to a class of strongly indefinite functionals, J. Differential Equations 125 (1996), no. 2, 521-547. crossref(new window)

5.
G. Fei, Multiple solutions of some nonlinear strongly resonant elliptic equations without the (PS) condition, J. Math. Anal. Appl. 193 (1995), no. 2, 659-670. crossref(new window)

6.
M. Lazzo, Nonlinear differential problems and Morse thoery, Nonlinear Anal. 30 (1997), no. 1, 169-176. crossref(new window)

7.
S. Li and J. Q. Liu, Computations of critical groups at degenerate critical point and applications to nonlinear differential equations with resonance, Houston J. Math. 25 (1999), no. 3, 563-582.

8.
S. Li and W. Zou, The Computations of the critical groups with an application to elliptic resonant problems at a higher eigenvalue, J. Math. Anal. Appl. 235 (1999), no. 1, 237-259. crossref(new window)

9.
S. Ma, Infinitely many solutions for cooperative elliptic systems with odd nonlinearity, Nonlinear Anal. 71 (2009), no. 5-6, 1445-1461. crossref(new window)

10.
S. Ma, Nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups, Nonlinear Anal. 73 (2010), no. 12, 3856-3872. crossref(new window)

11.
A. Pomponio, Asymptotically linear cooperative elliptic system: existence and multiplicity, Nonlinear Anal. 52 (2003), no. 3, 989-1003. crossref(new window)

12.
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. Math., vol. 65, Amer. Math. Soc., Providence, RI, 1986.

13.
M. Ramos and H. Tavares, Solutions with multiple spike patterns for an elliptic system, Calc. Var. Partial Differential Equations 31 (2008), no. 1, 1-25.

14.
M. Ramos and J. F. Yang, Spike-layered solutions for an elliptic system with Neumann boundary conditions, Trans. Amer. Math. Soc. 357 (2005), no. 8, 3265-3284. crossref(new window)

15.
M. Schechter and W. Zou, Weak linking theorems and Schrodinger equations with critical Sobolev exponent, ESAIM Control Optim. Calc. Var. 9 (2003), 601-619. crossref(new window)

16.
A. Szulkin and T.Weth, Ground state solutions for some indefinite variational problems, J. Functional Analysis 257 (2009), no. 12, 3802-3822. crossref(new window)

17.
C.-L. Tang and Q.-J. Gao, Elliptic resonant problems at higher eigenvalues with an unbounded nonlinear term, J. Differential Equations 146 (1998), no. 1, 56-66. crossref(new window)

18.
M. Willem, Minimax Theorems, Birkhauser, Boston, 1996.

19.
W. Zou, Solutions for resonant elliptic systems with nonodd or odd nonlinearities, J. Math. Anal. Appl. 223 (1998), no. 2, 397-417. crossref(new window)

20.
W. Zou, Multiple solutions for asymptotically linear elliptic systems, J. Math. Anal. Appl. 255 (2001), no. 1, 213-229. crossref(new window)

21.
W. Zou and S. Li, Nontrivial Solutions for resonant cooperative elliptic systems via computations of critical groups, Nonlinear Anal. 38 (1999), no. 2, Ser. A: Theory Methods, 229-247. crossref(new window)

22.
W. Zou and S. Li, Infinitely many solutions for Hamiltonian systems, J. Differential Equations 186 (2002), no. 1, 141-164. crossref(new window)