We consider the equation −ε2∆u+u=f(u) in a bounded, smooth domain Ω ⊂ R^N with homogeneous Dirichlet boundary conditions. We prove the existence of nodal solutions with multiple peaks concentrating at different points of Ω. The nonlinearity f grows superlinearly and subcritically. We do not require symmetry conditions on the geometry of the domain.
D'Aprile, T.c., Pistoia, A. (2011). Nodal solutions for some singularly perturbed Dirichlet problems. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363, 3601-3620 [10.1090/S0002-9947-2011-05221-9].
Nodal solutions for some singularly perturbed Dirichlet problems
D'APRILE, TERESA CARMEN;
2011-01-01
Abstract
We consider the equation −ε2∆u+u=f(u) in a bounded, smooth domain Ω ⊂ R^N with homogeneous Dirichlet boundary conditions. We prove the existence of nodal solutions with multiple peaks concentrating at different points of Ω. The nonlinearity f grows superlinearly and subcritically. We do not require symmetry conditions on the geometry of the domain.File in questo prodotto:
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