Abstract
We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator. The reaction has a parametric concave term and negative sublinear perturbation. In contrast to the case of a positive perturbation, we show that now for all big values of the parameter \(\lambda >0\), we have at least two positive solutions which do not vanish in the domain. In the process we prove a nonlinear maximum principle which is of independent interest.
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Communicated by Maria Alessandra Ragusa.
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The work was supported by NNSF of China Grant No. 12071413, NSF of Guangxi Grant No. 2018GXNSFDA138002.
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Liu, Z., Papageorgiou, N.S. Pairs of Positive Solutions for Nonhomogeneous Dirichlet Problems. Bull. Malays. Math. Sci. Soc. 44, 3969–3981 (2021). https://doi.org/10.1007/s40840-021-01124-9
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DOI: https://doi.org/10.1007/s40840-021-01124-9