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Monotonicity and Symmetry of Nonnegative Solutions to -Delta u = f(u) in Half-Planes and Strips

Abstract : We consider nonnegative solutions to -Delta u = f(u) in half-planes and strips, under zero Dirichlet boundary condition. Exploiting a rotating and sliding line technique, we prove symmetry and monotonicity properties of the solutions, under very general assumptions on the nonlinearity f. In fact, we provide a unified approach that works in all cases: f(0)< 0, f(0)= 0 or f(0)> 0. Furthermore, we make the effort to deal with nonlinearities f that may be not locally-Lipschitz continuous. We also provide explicit examples showing the sharpness of our assumptions on the nonlinear function f.
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https://hal-u-picardie.archives-ouvertes.fr/hal-03621417
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Soumis le : lundi 28 mars 2022 - 10:57:06
Dernière modification le : mercredi 14 septembre 2022 - 18:34:50

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Alberto Farina, Berardino Sciunzi. Monotonicity and Symmetry of Nonnegative Solutions to -Delta u = f(u) in Half-Planes and Strips. Advanced Nonlinear Studies, Walter de Gruyter GmbH, 2017, 17 (2, SI), pp.297-310. ⟨10.1515/ans-2017-0010⟩. ⟨hal-03621417⟩

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