Oscillatory radial solutions for subcritical biharmonic equations |
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Authors: | M Lazzo PG Schmidt |
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Institution: | a Dipartimento di Matematica, Università di Bari, via Orabona 4, 70125 Bari, Italy b Department of Mathematics and Statistics, Auburn University, AL 36849-5310, USA |
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Abstract: | It is well known that the biharmonic equation Δ2u=u|u|p−1 with p∈(1,∞) has positive solutions on Rn if and only if the growth of the nonlinearity is critical or supercritical. We close a gap in the existing literature by proving the existence and uniqueness, up to scaling and symmetry, of oscillatory radial solutions on Rn in the subcritical case. Analyzing the nodal properties of these solutions, we also obtain precise information about sign-changing large radial solutions and radial solutions of the Dirichlet problem on a ball. |
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Keywords: | 35J40 35J60 35B05 |
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