Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T02:51:41.297Z Has data issue: false hasContentIssue false

Existence of positive solutions for nonlocal and nonvariational elliptic systems

Published online by Cambridge University Press:  17 April 2009

Yujuan Chen
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, Peoples Republic of China
Hongjun Gao
Affiliation:
Department of Mathematics, Nantong University, Nantong 226007, Peoples Republic of China e-mail: nttccyj@ntu.edu.cn
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the paper we prove a result on the existence of positive solutions for a class of nonvariational elliptic system with nonlocal source by Galerkin methods and a fixed point theorem in finite dimensions. We establish another existence result by the super and subsolution method and a monotone iteration.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Alves, C.O. and Figureiredo, de D.G., ‘Nonvariational elliptic systems via Galerkin methods, function spaces, differential operators and nonlinear analysis’, in The Hans Tridbel Anniversary Volume (Birkhauser Berlag Base 1, Switzerland, 2003), pp. 4757.Google Scholar
[2]Correa, F.J.S.A., Menezes, D.B. Silbano and Ferreira, J., ‘On a class of problems involving a nonlocal operator’, Appl. Math. Comput. 147 (2004), 475489.Google Scholar
[3]Correa, F.J.S.A., ‘On positive solutions of nonlocal and nonvariational elliptic problems’, Nonlinear Anal. 59 (2004), 11471155.CrossRefGoogle Scholar
[4]Deng, W.B., Li, Y.X. and Xie, C.H., ‘Blow-up and global existence for a nonlocal degenerate parabolic system’, J. Math. Appl. 277 (2003), 199217.Google Scholar
[5]Drabek, P. and Hermandez, J., ‘Existence and uniqueness of positive solutions for some quasilinear elliptic problems’, Nonlinear Anal. 44 (2001), 189204.CrossRefGoogle Scholar
[6]Evans, L.C., Partial differential equations, Graduate Studies in Mathematics 19 (American Mathematical Society, Providence, R.I., 1998).Google Scholar
[7]Stanczy, R., ‘Nonlocal elliptic equations’, Nonlinear Anal. 47 (2001), 35793584.CrossRefGoogle Scholar