On the nodal lines of second eigenfunctions of the fixed membrane problem.
On the nodal set of eigenfunctions
On the nodal set of the second eigenfunction of the laplacian in symmetric domains in
We present a simple proof of the fact that if is a bounded domain in , , which is convex and symmetric with respect to orthogonal directions, , then the nodal sets of the eigenfunctions of the laplacian corresponding to the eigenvalues must intersect the boundary. This result was proved by Payne in the case for the second eigenfunction, and by other authors in the case of convex domains in the plane, again for the second eigenfunction.
On the non-convergence of successive approximations in the Darboux problem for the equation
On the nonconvergence of successive approximations in the theory of the equation
On the Nonexistence of a Hypersurface of Prescribed Mean Curvature with a Given Boundary.
On the nonhamiltonian character of shocks in 2-D pressureless gas
The paper deals with the 2-D system of gas dynamics without pressure which was introduced in 1970 by Ua. Zeldovich to describe the formation of largescale structure of the Universe. Such system occurs to be an intermediate object between the systems of ordinary differential equations and hyperbolic systems of PDE. The main its feature is the arising of singularities: discontinuities for velocity and d-functions of various types for density. The rigorous notion of generalized solutions in terms of...
On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity
We consider the Neumann problem for the equation , u ∈ H¹(Ω), where Q is a positive and continuous coefficient on Ω̅ and λ is a parameter between two consecutive eigenvalues and . Applying a min-max principle based on topological linking we prove the existence of a solution.
On the nonlinear Neumann problem involving the critical Sobolev exponent and Hardy potential.
In this paper we investigate the solvability of some Neumann problems involving the critical Sobolev and Hardy exponents.
On the nonlinear Neumann problem with critical and supercritical nonlinearities [Book]
On the nonlinear stabilization of the wave equation
We obtain a precise decay estimate of the energy of the solutions to the initial boundary value problem for the wave equation with nonlinear internal and boundary feedbacks. We show that a judicious choice of the feedbacks leads to fast energy decay.
On the nonrelativistic limit of the Dirac hamiltonian
On the non-uniqueness of weak solution of the Euler equations
On the number of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds.
On the number of positive solutions of singularly perturbed 1D nonlinear Schrödinger equations
We study singularly perturbed 1D nonlinear Schrödinger equations (1.1). When has multiple critical points, (1.1) has a wide variety of positive solutions for small and the number of positive solutions increases to as . We give an estimate of the number of positive solutions whose growth order depends on the number of local maxima of . Envelope functions or equivalently adiabatic profiles of high frequency solutions play an important role in the proof.
On the number of positive solutions of some weakly nonlinear equations on annular regions.
On the number of single-peak solutions of the nonlinear Schrödinger equation
On the numerical approximation of first-order Hamilton-Jacobi equations
Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
On the Numerical Errors in One Step Algorithms for Time Dependent Problems.
On the Numerical Integration of the Heat Equation.