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The nodal line of the second eigenfunction of the Robin Laplacian in $\mathbb{R}^2$ can be closed
Laplacian eigenfunction nodal line Robin boundary
2010/12/13
We construct a multiply connected domain in R2 for which the second eigenfunction of the Laplacian with Robin boundary condi-tions has an interior nodal line. In the process, we adapt a bound of Donne...
On the construction of the KP line-solitons and their interactions
KPequation line-solitons t-function
2010/4/7
The line-soliton solutions of the Kadomtsev--Petviashvili (KP) equation are investigated in this article using the tau-function formalism. In particular, the Wronskian and the Grammian forms of the ta...
Positive solutions for Second-Order Boundary Value Problem with Integral Boundary Conditions at Resonance on a Half-Line
Boundary value problem Resonance Cone Positive solution Coincidence
2010/1/22
This paper deals with the second order boundary value problem with integral boundary conditions on a half-line: a.e. in A new result on the existence of positive solutions is obta...
Hardy-Type Inequalities On The Real Line
Real Hardy's inequality Inequalities in $H_1$ spaces
2010/1/22
We prove a certain type of inequalities concerning the integral of the Fourier transform of a function integrable on the real line.