Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions
Por:
Saldaña A., Tavares H.
Publicada:
1 ene 2018
Resumen:
We study existence, regularity, and qualitative properties of solutions to the system - u=|v|q-1v in O,- v=|u|p-1u in O,??u=??v=0 on ?O, with O?RN bounded; in this setting, all nontrivial solutions are sign changing. Our proofs use a variational formulation in dual spaces, considering sublinear pq<1 and superlinear pq>1 problems in the subcritical regime. In balls and annuli we show that least energy solutions (l.e.s.) are foliated Schwarz symmetric and, due to a symmetry-breaking phenomenon, l.e.s. are not radial functions; a key element in the proof is a new Lt-norm-preserving transformation, which combines a suitable flipping with a decreasing rearrangement. This combination allows us to treat annular domains, sign-changing functions, and Neumann problems, which are non-standard settings to use rearrangements and symmetrizations. In particular, we show that our transformation diminishes the (dual) energy and, as a consequence, radial l.e.s. are strictly monotone. We also study unique continuation properties and simplicity of zeros. Our theorems also apply to the scalar associated model, where our approach provides new results as well as alternative proofs of known facts. © 2018 Elsevier Inc.
Filiaciones:
Saldaña A.:
Institut für Analysis, Karlsruhe Institute for Technology, Englerstrasse 2, Karlsruhe, 76131, Germany
Tavares H.:
CAMGSD, Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, Lisboa, 1049-001, Portugal
Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa, Edifício C6, Piso 1, Campo Grande, Lisboa, 1749-016, Portugal
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