# Questions tagged [nonlinear-eigenvalue]

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### Bifurcation points in parametric Hammerstein Integral equation

I am a theoretical physicist working on integrable systems, hence I preemptively ask forgiveness for the eventual lack of mathematical rigor. My question concerns the properties of a particular ...
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I am interested in a flame propagation in 1D which is governed by a nonlinear convection-diffusion-reaction equation system: $$u_t+C(u)u_x+(D(u)\cdot u_x)_x + R(u) = 0,x\in (-\infty,+\infty) \\ u(-\... 2 votes 0 answers 217 views ### The nonlinear operator defined as the commutator of a matrix and a nonlinear operator In my studies of applied analysis and applied linear algebra, this interesting problem and concept came up: Let us consider the space of all  m \times n  real matrices, and define a scalar ... 6 votes 0 answers 178 views ### Is this "stretched eigenvector" studied? (If so, what are its properties?) An eigenvector is defined by$$ \lambda \mathbf{v} = A\mathbf{v}.\tag{1} $$But suppose I change this to$$ \lambda \mathbf{v} = A\mathbf{v}^\alpha,\tag{2} $$for real \alpha\ne 1, where \mathbf{v}^... 1 vote 1 answer 89 views ### Polynomial Eigenvalue Problem with few non-zero coefficients Let us define a diagonal matrix \mathbf{D}(\lambda) = diag(\lambda^{m_1}, \dots, \lambda^{m_n}) with \lambda\in\mathbb{C} and positive integers m_1, \dots, m_n. The generalized characteristic ... 6 votes 1 answer 1k views ### First eigenfunction of p=3-Laplacian of a square domain in \Bbb R^2 : reference for any work on this? In the last few decades, lots of work on first eigenfunction of p-Laplace with Dirichlet and other boundary conditions. But I couldn't find much on periodic boundary conditions. I have computed the ... 2 votes 1 answer 278 views ### Simultaneous triangularization of two diagonal matrices and a symmetric matrix I have the following quadratic eigenvalue problem: \det(\lambda^2M + \lambda D + J)=0 where, M and D are both n \times n real diagonal matrix with positive diagonal entries; J is 1) a ... 5 votes 1 answer 127 views ### How does one go from convexity to submodularity? If I have a function which is convex in the hypercube, [-1,1]^n then when would it imply that its restriction to \{-1,1\}^n is submodular? It would be helpful is someone can share some specific ... 5 votes 2 answers 194 views ### significance of the Fučík spectrum The Fučík spectrum seems to gain momentum among people working on spectral theory, with almost 300 articles published on this topic over the last 5 years, according to Google scholar. There exist ... 2 votes 3 answers 920 views ### Non-linear state-space model system stability using Lyapunov? I have a non-linear system modelled in state-space as follow:$$ \mathbf {\dot x} = \mathbf A(x) \mathbf x  I need to find out if this system is stable, so I was thinking in using the Lyapunov ...
Suppose we have a quadratic eigenvalue problem $(A_{0}+\lambda A_{1}+ \lambda^{2} A_{2})x=0$. I'd to know if there are conditions under which the problem is known to have a small number of distinct ...
Suppose you have an equation of the form $Ax=f(x)$, where $A$ is a $n \times n$ matrix, $x$ is a vector of length $n$ and $f(\cdot)$ is some function. Is there a name for this sort of problem?