Abstract
We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart [22] and whose study is motivated by models in Nonlinear Optics. We establish sufficient conditions for the existence of at least one or two non-negative solutions. Our analysis considers the cases when the reaction has either a sublinear or a linear growth. In the sublinear case, we also prove a nonexistence property. The proofs combine energy estimates and variational methods.
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Acknowledgements
This work was initiated during a visit of the second author to the University of Franche—Comté in March 2013. The second author thanks the University of Franche—Comté for the financial support. The authors are grateful to Professor Haim Brezis for his valuable comments on a previous version of this paper. The first author also thanks M. L. M. Carvalho and E. D. Silva for discussing with him their results in [8, 10] connected with Lemma 3.5 and D. Arcoya and J. Giacomoni for useful remarks.
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Jeanjean, L., Rădulescu, V.D. Nonhomogeneous quasilinear elliptic problems: linear and sublinear cases. JAMA 146, 327–350 (2022). https://doi.org/10.1007/s11854-021-0170-7
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DOI: https://doi.org/10.1007/s11854-021-0170-7