We prove the existence of nodal solutions for −Δu = ρ sinh u with Dirichlet boundary conditions in bounded, 2D, smooth and non-smooth domains. Indeed, for ρ positive and small enough, we show that there exist at least two pairs of solutions, which change sign exactly once, whose nodal lines intersect the boundary.
Existence and qualitative properties of concentrating solutions for the sinh-Poisson equation / Bartolucci, D; Pistoia, Angela. - In: JOURNAL OF APPLIED MATHEMATICS. - ISSN 1110-757X. - STAMPA. - 72:(2007), pp. 706-729. [10.1093/imamat/hxm012]
Existence and qualitative properties of concentrating solutions for the sinh-Poisson equation
PISTOIA, Angela
2007
Abstract
We prove the existence of nodal solutions for −Δu = ρ sinh u with Dirichlet boundary conditions in bounded, 2D, smooth and non-smooth domains. Indeed, for ρ positive and small enough, we show that there exist at least two pairs of solutions, which change sign exactly once, whose nodal lines intersect the boundary.File allegati a questo prodotto
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
