On multiple solutions of a nonlinear Neumann problem

On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem

In this paper, in order to numerically solve for multiple positive solutions to a singularly perturbed Neumann boundary value problem in mathematical biology and other applications, a local minimax method is modified with new local mesh refinement and other strategies. Algorithm convergence and other related properties are verified. Motivated by the numerical algorithm and convinced by the nume...

Existence and Continuation of Solutions for a Nonlinear Neumann Problem

In this article we study the existence, continuation and bifurcation from infinity of nonconstant solutions for a nonlinear Neumann problem. We apply the LeraySchauder degree and the degree for SO(2)-equivariant gradient operators defined by the second author in [21].

Entropy Solutions for Nonlinear Elliptic Anisotropic Homogeneous Neumann Problem

Three Solutions for a Neumann Problem

In this paper we consider a Neumann problem of the type (Pλ) 8< : −∆u = α(x)(|u|q−2u− u) + λf(x, u) in Ω, ∂u ∂ν = 0 on ∂Ω. Applying the theory developed in [13], we establish, under suitable assumptions, the existence of an open interval Λ ⊆ R and of a positive real number %, such that, for each λ ∈ Λ, problem (Pλ) admits at least three weak solutions in W 1,2(Ω) whose norms are less than %. Le...

Special solutions of nonlinear von Neumann equations

We consider solutions of the non-linear von Neumann equation involving Jacobi’s elliptic functions sn, cn, and dn, and 3 linearly independent operators. In two cases one can construct a state-dependent Hamiltonian which is such that the corresponding non-linear von Neumann equation is solved by the given density operator. We prove that in a certain context these two cases are the only possibili...