We consider the equation -epsilon(2)Delta u+u = f(u) in a bounded, smooth domain Omega subset of R(N) with homogeneous Dirichlet boundary conditions. We prove the existence of nodal solutions with multiple peaks concentrating at different points of Omega. The nonlinearity f grows superlinearly and subcritically. We do not require symmetry conditions on the geometry of the domain.
NODAL SOLUTIONS FOR SOME SINGULARLY PERTURBED DIRICHLET PROBLEMS / Teresa, D'Aprile; Pistoia, Angela. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 363:07(2011), pp. 3601-3620. [10.1090/s0002-9947-2011-05221-9]
NODAL SOLUTIONS FOR SOME SINGULARLY PERTURBED DIRICHLET PROBLEMS
PISTOIA, Angela
2011
Abstract
We consider the equation -epsilon(2)Delta u+u = f(u) in a bounded, smooth domain Omega subset of R(N) with homogeneous Dirichlet boundary conditions. We prove the existence of nodal solutions with multiple peaks concentrating at different points of Omega. The nonlinearity f grows superlinearly and subcritically. We do not require symmetry conditions on the geometry of the domain.File allegati a questo prodotto
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