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Article Dans Une Revue Advanced Nonlinear Studies Année : 2017

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

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Résumé

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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Dates et versions

hal-03621417 , version 1 (28-03-2022)

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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, 2017, 17 (2, SI), pp.297-310. ⟨10.1515/ans-2017-0010⟩. ⟨hal-03621417⟩
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