相关论文: On Bobkov-Tanaka type spectrum for the double-phas…

The dispersive interaction between a two-level atom and a quantized field is studied. We consider besides a time dependent linear amplification and dissipative processes. In order to solve the master equation for this system, we use…

We study parametric double phase problems involving superlinear nonlinearities with a growth that need not necessarily be polynomial. Based on truncation and comparison methods the existence of two constant sign solutions is shown provided…

We address the question whether there is a three-dimensional bounded domain such that the Neumann--Poincar\'e operator defined on its boundary has infinitely many negative eigenvalues. It is proved in this paper that tori have such a…

This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…

We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…

For $\xi \in \big(0, {1/2} \big)$, we denote by $E_{\xi}$ the perfect symmetric set associated to $\xi$, that is $$ E_{\xi} = \Big\{\exp \big(2i \pi (1-\xi) \dsp \sum_{n = 1}^{+\infty} \epsilon_{n} \xi^{n-1} \big) : \epsilon_{n} = 0…

This article establishes a bilinear embedding for second-order divergence-form operators with complex coefficients, characterized by the simultaneous presence of first-order terms and negative potentials. This work provides a further…

We give a new region of existence of solutions to the superhomogeneous Dirichlet problem $$ \quad \begin{array}{l} -\Delta_{p} u= v^\delta\quad v>0\quad {in}\quad B,\cr -\Delta_{q} v = u^{\mu}\quad u>0\quad {in}\quad B, \cr u=v=0 \quad…

We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the…

In this paper we prove the existence of a weak solution to a doubly nonlinear parabolic fractional $p$-Laplacian equation, which has general doubly non-linearlity including not only the Sobolev subcritical/critical/supercritical cases but…

Using a variational technique we guarantee the existence of a solution to the \emph{resonant Lane-Emden} problem $-\Delta_p u=\lambda |u|^{q-2}u$, $u|_{\partial\Omega}=0$ if and only if a solution to $-\Delta_p u=\lambda |u|^{q-2}u+f$,…

In this note, we consider the Dirac operator $D$ on a Riemannian symmetric space $M$ of noncompact type. Using representation theory we show that $D$ has point spectrum iff the $\hat A$-genus of its compact dual does not vanish. In this…

In this paper, we consider the existence and nonexistence of positive solution for a Neumann problem with double critical exponents and fast increasing weighted in half-space. This problem is closely related to the study of self-similar…

We study fractal dimension properties of singular Jacobi operators. We prove quantitative lower spectral/quantum dynamical bounds for general operators with strong repetition properties and controlled singularities. For analytic…

On the half line $[0,\infty)$ we study first order differential operators of the form $B 1/i d/(dx) + Q(x)$, where $B:=\mat{B_1}{0}{0}{-B_2}$, $B_1,B_2\in M(n,\C)$ are self--adjoint positive definite matrices and $Q:\R_+\to M(2n,\C)$,…

Analyzing the point spectrum, i.e. bound state energy eigenvalue, of the Dirac delta function in two and three dimensions is notoriously difficult without recourse to regularization or renormalization, typically both. The reason for this in…

We describe a simple but surprisingly effective technique of obtaining spectral multiplier results for abstract operators which satisfy the finite propagation speed property for the corresponding wave equation propagator. We show that, in…

We prove the existence of time-periodic, small amplitude solutions of autonomous quasilinear or fully nonlinear completely resonant pseudo-PDEs of Benjamin-Ono type in Sobolev class. The result holds for frequencies in a Cantor set that has…

Let $T$ be a self-adjoint operator in a Hilbert space $H$ with domain $\mathcal D(T)$. Assume that the spectrum of $T$ is confined in the union of disjoint intervals $\Delta_k =[\alpha_{2k-1},\alpha_{2k}]$, $k\in \mathbb{Z}$, and $$…

The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators…