MR
G. A. AFROUZI, N. T. CHUNG and S. SHAKERI
G. A. AFROUZI, N. T. CHUNG and S. SHAKERI
Existence and Non-Existence Results for Nonlocal Elliptic Systems via Sub-Supersolution Method
Funkcialaj Ekvacioj. Serio Internacia
59
2016
303--313
http://fe.math.kobe-u.ac.jp/FE/FullPapers/59-3/59_303.pdf
http://www.ams.org/mathscinet-getitem?mr=MR
In this paper, using a sub-supersolution argument, we prove an existence result on a positive weak solution for a class of nonlocal elliptic systems in bounded domains.
Nonlocal elliptic systems, Existence, Non-Existence, Positive solution, Sub-supersolution method.
35D05, 35J60.
59-303
2016
Existence and Non-Existence Results for Nonlocal Elliptic Systems via Sub-Supersolution Method
G. A. AFROUZI, N. T. CHUNG and S. SHAKERI
G. A. AFROUZI, N. T. CHUNG and S. SHAKERI
1
Alves, C. O.; Corrêa, F. J. S. A.
On existence of solutions for a class of problem involving a nonlinear operator
Comm. Appl. Nonlinear Anal.
8
2001
43-56
MR1837101
2
Azzouz, N.; Bensedik, A.
Existence results for an elliptic equation of Kirchhoff-type with changing sign data
Funkcial. Ekvac.
55
2012
55-66
MR2976042
2976042
3
Chipot, M.; Lovat, B.
Some remarks on nonlocal elliptic and parabolic problems
Nonlinear Anal.
30
1997
4619-4627
MR1603446
4
Corrêa, F. J. S. A.; Figueiredo, G. M.
On an elliptic equation of $p$-Kirchhoff type via variational methods
Bull. Austral. Math. Soc.
74
2006
263-277
MR2260494
5
Corrêa, F. J. S. A.; Figueiredo, G. M.
On a $p$-Kirchhoff equation via Krasnoselskii's genus
Appl. Math. Lett.
22
2009
819-822
MR2523587
6
Hai, D. D.; Shivaji, R.
An existence result on positive solutions for a class of $p$-Laplacian systems
Nonlinear Anal.
56
2004
1007-1010
MR2038734
7
Han, X.; Dai, G.
On the sub-supersolution method for $p(x)$-Kirchhoff type equations
J. Inequal. Appl.
2012:283
2012
11pp
MR3017321
8
Kirchhoff, G.
Mechanik
Teubner, Leipzig, Germany
1883
9
Ma, T. F.
Remarks on an elliptic equation of Kirchhoff type
Nonlinear Anal.
63
2005
1967-1977
10
Perera, K.; Zhang, Z.
Nontrivial solutions of Kirchhoff-type problems via the Yang index
J. Differential Equations
221
2006
246-255
MR2193850
11
Ricceri, B.
On an elliptic Kirchhoff-type problem depending on two parameters
J. Global Optim.
46
2010
543-549
MR2601787
12
Sun, J. J.; Tang, C. L.
Existence and multiplicity of solutions for Kirchhoff type equations
Nonlinear Anal.
74
2011
1212-1222
MR2746801
13
Zhang, Z.; Perera, K.
Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow
J. Math. Anal. Appl.
317
2006
456-463
MR2208932