Abstract
We consider a nonlinear noncoercive elliptic equation driven by the p-Laplacian. We show that if the \({L^{\infty}}\)-perturbation has small norm, then the problem admits a positive solution. Moreover, if the \({L^{\infty}}\)-perturbation is nonzero and nonnegative, then we find two positive solutions. Also, we consider a class of semilinear equations with an indefinite and unbounded potential. Using critical groups, we show that there is a nontrivial solution and under a global sign condition, we show that this solutions is nodal. Our results extend and improve a recent work of Rădulescu (Discr. Cont. Dyn. Syst. Ser. S , 5:845–856, [14]).
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Papageorgiou, N.S., Rădulescu, V.D. On noncoercive elliptic problems. Nonlinear Differ. Equ. Appl. 23, 42 (2016). https://doi.org/10.1007/s00030-016-0394-x
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DOI: https://doi.org/10.1007/s00030-016-0394-x