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Existence of bounded solutions for nonlinear elliptic equations in unbounded domains

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract.

In this paper we study the existence of bounded weak solutions for some nonlinear Dirichlet problems in unbounded domains. The principal part of the operator behaves like the p-laplacian operator, and the lower order terms, which depend on the solution u and its gradient ∇ u, have a power growth of order p−1 with respect to these variables, while they are bounded in the x variable. The source term belongs to a Lebesgue space with a prescribed asymptotic behaviour at infinity.

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Authors and Affiliations

  1. Dipartimento di Metodi e Modelli, Matematici per le Scienze Applicate, Università di Roma I “La Sapienza”, Via Antonio Scarpa 16, 00161, Roma, Italy

    A. Dall’aglio, V. De Cicco & D. Giachetti

  2. Laboratoire de Mathématiques Appliquées, Université de Versailles St. Quentin, 45 Avenue des Etats Unis, 78035, Versailles Cedex, France

    J. -P. Puel

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  1. A. Dall’aglio
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  2. V. De Cicco
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  3. D. Giachetti
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  4. J. -P. Puel
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Correspondence to A. Dall’aglio.

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Dall’aglio, A., De Cicco, V., Giachetti, D. et al. Existence of bounded solutions for nonlinear elliptic equations in unbounded domains. Nonlinear differ. equ. appl. 11, 431–450 (2004). https://doi.org/10.1007/s00030-004-1070-0

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  • DOI: https://doi.org/10.1007/s00030-004-1070-0

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