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constant-sign solutions

Proceedings of the Edinburgh Mathematical Society (1)

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Constant-Sign and Nodal Solutions to a Dirichlet Problem with p-Laplacian and Nonlinearity Depending on a Parameter
Salvatore A. Marano, Nikolaos S. Papageorgiou
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 57 / Issue 2 / June 2014

Published online by Cambridge University Press:

05 September 2013, pp. 521-532
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A homogeneous Dirichlet problem with p-Laplacian and reaction term depending on a parameter λ > 0 is investigated. At least five solutions—two negative, two positive and one sign-changing (namely, nodal)—are obtained for all λ sufficiently small by chiefly assuming that the involved non-linearity exhibits a concave-convex growth rate. Proofs combine variational methods with truncation techniques.