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BOUNDED MULTIPLE SOLUTIONS FOR $p$-LAPLACIAN PROBLEMS WITH ARBITRARY PERTURBATIONS

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  26 February 2015

FRANCESCA FARACI  and
LIN ZHAO
FRANCESCA FARACI*
Affiliation:
Department of Mathematics and Computer Sciences, University of Catania, Italy email ffaraci@dmi.unict.it
LIN ZHAO
Affiliation:
School of Sciences, China University of Mining and Technology, Xuzhou 221116, China School of Mathematics and Statistics, Lanzhou University, China email zhjz9332003@gmail.com
*
✉ffaraci@dmi.unict.it
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Abstract

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In the present paper we deal with the existence of multiple solutions for a quasilinear elliptic problem involving an arbitrary perturbation. Our approach, based on an abstract result of Ricceri, combines truncation arguments with Moser-type iteration technique.

Keywords

variational methodsbounded multiple solutionsquasilinear elliptic equationsMoser iteration techniquearbitrary perturbations

MSC classification

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35J62: Quasilinear elliptic equations 35J92: Quasilinear elliptic equations with $p$-Laplacian

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 2 , October 2015 , pp. 175 - 185
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Anello, G., ‘Existence of solutions for a perturbed Dirichlet problem without growth conditions’, J. Math. Anal. Appl. 330 (2007), 1169–1178.CrossRefGoogle Scholar
Chen, S. and Li, S., ‘On a nonlinear elliptic eigenvalue problem’, J. Math. Anal. Appl. 307 (2005), 691–698.CrossRefGoogle Scholar
Iturriaga, L., Lorca, S. and Massa, E., ‘Positive solutions for the p-Laplacian involving critical and supercritical nonlinearities with zeros’, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 763–771.Google Scholar
Lieberman, G. M., ‘Boundary regularity for solutions of degenerate elliptic equations’, Nonlinear Anal. 12 (1988), 1203–1219.CrossRefGoogle Scholar
Lorca, S. and Ubilla, P., ‘Partial differential equations involving subcritical, critical and supercritical nonlinearities’, Nonlinear Anal. 56 (2004), 119–131.CrossRefGoogle Scholar
Miyajima, S., Motreanu, D. and Tanaka, M., ‘Multiple existence results of solutions for the Neumann problems via super- and sub-solutions’, J. Funct. Anal. 262 (2012), 1921–1953.CrossRefGoogle Scholar
Ricceri, B., ‘A further three critical points theorem’, Nonlinear Anal. 71 (2009), 4151–4157.CrossRefGoogle Scholar
Zhao, L. and Zhao, P., ‘The existence of three solutions for p-Laplacian problems with critical and supercritical growth’, Rocky Mountain J. Math. 44 (2014), 1383–1397.CrossRefGoogle Scholar