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Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with p-Laplacian

Publication date: 20.12.2012

Schedae Informaticae, 2012, Volume 21, pp. 27 - 40

https://doi.org/10.4467/20838476SI.12.002.0812

Authors

,
Leszek Gasiński
Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland
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Nikolaos S. Papageorgiou
National Technical University, Athens, Greece
All publications →

Titles

Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with p-Laplacian

Abstract

We consider a nonlinear Neumann elliptic equation driven by the p-Laplacian and a Carathéodory perturbation. The energy functional of the problem need not be coercive. Using variational methods we prove an existence theorem and a multiplicity theorem, producing two nontrivial smooth solutions. Our formulation incorporates strongly resonant equations..

References

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Filippakis M., Gasinski L., Papageorgiou N.S.; Multiplicity result for nonlinear Neu- mann problems, Canad. J. Math. 58, 2006, pp. 64{92.

Gasinski L., Papageorgiou N.S.; Nonlinear Analysis, Chapman and Hall/CRC Press, Boca Raton, FL, 2006.

Lieberman G.M.; Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. 12, 1988, pp. 1203{1219.

Motreanu D., Papageorgiou N.S.; Existence and multiplicity of solutions for Neumann problems, J. Dierential Equations 232, 2007, pp. 1{35.

O'Regan D., Papageorgiou N.S.; The existence of two nontrivial solutions via homolog- ical local linking for the non-coercive p-Laplacian Neumann problem, Nonlinear Anal. 70, 2009, pp. 4386{4392.

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Information

Information: Schedae Informaticae, 2012, Volume 21, pp. 27 - 40

Article type: Original article

Titles:

Polish:

Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with p-Laplacian

English:

Existence and Multiplicity of Solutions for Noncoercive Neumann Problems with p-Laplacian

Authors

Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland

National Technical University, Athens, Greece

Published at: 20.12.2012

Article status: Open

Licence: None

Percentage share of authors:

Leszek Gasiński (Author) - 50%
Nikolaos S. Papageorgiou (Author) - 50%

Article corrections:

-

Publication languages:

English