On the existence and profile of nodal solutions for a two-dimensional elliptic problem with large exponent in nonlinearity
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Date
2007
Journal Title
Journal ISSN
Volume Title
Publisher
WILEY
Abstract
We study the existence of nodal solutions to the boundary value problem -Delta u = \u\(p-1)u in a bounded, smooth domain Omega in R-2, with homogeneous Dirichlet boundary condition, when p is a large exponent. We prove that, for p large enough, there exist at least two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of Omega.
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Keywords
QUALITATIVE PROPERTIES, SINGULAR LIMITS, EQUATIONS