We consider the semilinear Lane Emden problem {-Delta u = vertical bar u vertical bar(p-1)u in Omega, u = 0 on partial derivative Omega (epsilon(p)) where Omega is a smooth bounded simply connected domain in R-2, invariant by the action of a finite symmetry group G. We show that if the orbit of each point in Omega, under the action of the group G, has cardinality greater than or equal to 4 then, for p sufficiently large, there exists a sign-changing solution of (epsilon(p)) with two nodal regions whose nodal line does not touch partial derivative Omega. This result is proved as a consequence of an analogous result for the associated parabolic problem. (C) 2013 Elsevier Inc. All rights reserved.

Sign-changing solutions of Lane Emden problems with interior nodal line and semilinear heat equations / DE MARCHIS, Francesca; Ianni, Isabella; Pacella, Filomena. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 254:8(2013), pp. 3596-3614. [10.1016/j.jde.2013.01.037]

Sign-changing solutions of Lane Emden problems with interior nodal line and semilinear heat equations

DE MARCHIS, FRANCESCA;Isabella Ianni;PACELLA, Filomena
2013

Abstract

We consider the semilinear Lane Emden problem {-Delta u = vertical bar u vertical bar(p-1)u in Omega, u = 0 on partial derivative Omega (epsilon(p)) where Omega is a smooth bounded simply connected domain in R-2, invariant by the action of a finite symmetry group G. We show that if the orbit of each point in Omega, under the action of the group G, has cardinality greater than or equal to 4 then, for p sufficiently large, there exists a sign-changing solution of (epsilon(p)) with two nodal regions whose nodal line does not touch partial derivative Omega. This result is proved as a consequence of an analogous result for the associated parabolic problem. (C) 2013 Elsevier Inc. All rights reserved.
superlinear elliptic boundary value problem; parabolic flow; nodal set; sign-changing solution
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Sign-changing solutions of Lane Emden problems with interior nodal line and semilinear heat equations / DE MARCHIS, Francesca; Ianni, Isabella; Pacella, Filomena. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 254:8(2013), pp. 3596-3614. [10.1016/j.jde.2013.01.037]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/516934
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