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Khademloo, S.; Valipour, E.; Babakhani, A.

Multiplicity of positive solutions for a second-order elliptic system of Kirchhoff type. (English) Zbl 1472.35153

Abstr. Appl. Anal. 2014, Article ID 280130, 9 p. (2014).
Summary: We study elliptic problems of Kirchhoff type in \(\Omega \subset \mathbb{R}^N\) (\(N \geq 3\)). Using variational tools, we establish the existence of at least two nontrivial and nonnegative solutions.

Cited in 2 Documents

MSC:

35J57 Boundary value problems for second-order elliptic systems
35J62 Quasilinear elliptic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A15 Variational methods applied to PDEs

Keywords:

Kirchhoff-type system; Dirichlet condition; existence; variational methods
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\textit{S. Khademloo} et al., Abstr. Appl. Anal. 2014, Article ID 280130, 9 p. (2014; Zbl 1472.35153)
Full Text: DOI

References:

[1] Kirchhoff, G. R., Vorlesungen über mathematische Physik: Mechanik (1883), Leipzig, Germany: B.G. Teubner, Leipzig, Germany
[2] Julio, F.; Correa, S. A.; Figueiredo, G. M., On an elliptic equation of p-Kirchhoff type via variational methods, Bulletin of the Australian Mathematical Society, 74, 246-277 (2006) · Zbl 1108.45005
[3] Chen, C. Y.; Kuo, Y. C.; Wu, T. F., The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions, Journal of Differential Equations, 250, 4, 1876-1908 (2011) · Zbl 1214.35077
[4] Jin, J. H.; Wu, X., Infinitly many radial solutions for Kirchhoff type problem in \(R^N\), Journal of Mathematical Analysis and Applications, 369, 2, 564-574 (2010) · Zbl 1196.35221
[5] He, X. M.; Zou, W. M., Infinitely many positive solutions for Kirchhoff-type problems, Nonlinear Analysis, Theory, Methods and Applications, 70, 3, 1407-1414 (2009) · Zbl 1157.35382
[6] Perera, K.; Zhang, Z. T., Nontrivial solutions of Kirchhoff-type problems via the Yang index, Journal of Differential Equations, 221, 1, 246-255 (2006) · Zbl 1357.35131
[7] Ferrara, M.; Khademloo, S.; Heidarkhani, S., Multiplicity results for perturbed fourth-order Kirchhoff type elliptic problems, Applied Mathematics and Computation, 234, 316-325 (2014) · Zbl 1305.35046
[8] Julio, F.; Correa, S. A.; Nascimento, R. G., On a nonlocal elliptic system of \(p\)-Kirchhoff-type under Neumann boundary condition, Mathematical and Computer Modelling, 49, 3-4, 598-604 (2009) · Zbl 1173.35445
[9] Willem, M., Minimax Theorems (1996), Boston, Mass, USA: Birkhäuser, Boston, Mass, USA · Zbl 0856.49001
[10] Shen, Y.; Zhang, J., Multiplicity of positive solutions for a semilinear \(p\)-Laplacian system with Sobolev critical exponent, Nonlinear Analysis. Theory, Methods & Applications, 74, 4, 1019-1030 (2011) · Zbl 1206.35098
[11] Brown, K. J.; Wu, T.-F., A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function, Journal of Mathematical Analysis and Applications, 337, 2, 1326-1336 (2008) · Zbl 1132.35361
[12] Wu, T. F., A semilinear elliptic equations involving nonlinear bou ndary codition and signchanging potential, Electronic Journal of Differential Equations, 131, 1-15 (2006)
[13] Brézis, H.; Lieb, A., A relation between pointwise convergence of functions and convergence of functionals, Proceedings of the American Mathematical Society, 88, 486-490 (1983) · Zbl 0526.46037
[14] Hsu, T.-S., Multiple positive solutions for a critical quasilinear elliptic system with concave-convex nonlinearities, Nonlinear Analysis: Theory, Methods & Applications, 71, 7-8, 2688-2698 (2009) · Zbl 1167.35356
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