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.
Bartolucci, D., Pistoia, A. (2007). Existence and qualitative properties of concentrating solutions for the sinh-Poisson equation. IMA JOURNAL OF APPLIED MATHEMATICS, 72, 706-729 [10.1093/imamat/hxm012].
Existence and qualitative properties of concentrating solutions for the sinh-Poisson equation
BARTOLUCCI, DANIELE;
2007-01-01
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 in questo prodotto:
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