Abstract
This chapter is concerned with parametric Dirichlet boundary value problems involving the p-Laplacian operator. Specifically, this chapter gives an account of recent results that establish the existence and multiplicity of solutions according to different types of nonlinearities in the problem. More precisely, we focus on problems exhibiting nonlinearities of concave–convex type and nonlinearities that are asymptotically \((p-1)\)-linear. In each situation, we point out significant qualitative properties of the solutions, especially, we establish the existence of sign-changing (that is, nodal) solutions.
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Acknowledgements
The second author is supported by a Marie Curie Intra-European Fellowship for Career Development within the European Community’s 7th Framework Program (Grant Agreement No. PIEF-GA-2010-274519).
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Motreanu, D., Motreanu, V. (2014). Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters. In: Rassias, T. (eds) Handbook of Functional Equations. Springer Optimization and Its Applications, vol 95. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1246-9_15
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