Let ϵ>0, and let bϵ=b−ϵ. Then we consider the following regularized problem for (Pλ).

We investigate the problem $$-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \mbox{ in } \Omega, \quad \frac{\partial u}{\partial \mathbf{n}} = 0 …

This paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolutio…

By applying Darboux-Crum transformations to a Lax pair formulation of the Korteweg-de Vries (KdV) equation, we construct new sets of multi-soliton so…

The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limi…

Whether it is possible to close the gap between the factors of approximation of Box Cover and Orthogonal Polygon Covering has been a long standing open question [KumarR03]. The Minimum Coverage Kernel problem, intermediate between those two, has the…

We consider the Minimum Coverage Kernel problem: given a set $B$ of $d$-dimensional boxes, find a subset of $B$ of minimum size covering the same reg…

In this work we address the study of movement of charged particles in the background of charged black holes with non-trivial asymptotic behavior. We …

In this paper we study the consistency of a cosmological model, described by a novel exact analytic solution of a universe filled with a dissipative …

The authors thank Georgi Raikov for suggesting this problem and useful discussions.

We consider the Schr\"odinger operator with constant magnetic field defined on the half-plane with a Dirichlet boundary condition, $H_0$, and a decay…

We study experimentally the interaction between two solitary waves that approach one to another in a linear chain of spheres interacting via the Hert…

The following a priori upper bound of λ for positive solutions of (Qλ,ϵ) follows from [13, Proposition 6.1]:

We proceed with the investigation of the problem $(P_\lambda): $ $-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \ \mbox{ in } \Omega, \ \ \frac{…

An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve…

We investigate a special class of the $\mathcal{PT}$-symmetric quantum models being perfectly invisible zero-gap systems with a unique bound state at…

Topological solitons are relevant in several areas of physics [1]. Recently, these configurations have been investigated in contexts as diverse as hy…

Given a convex $n$-gon, we can draw $n$ disks (called side disks) where each disk has a different side of the polygon as diameter and the midpoint of…

Before proceeding to the proofs of our main results, we prove a partial positivity result on the boundary for nontrivial non-negative solutions of (Pλ):

We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonli…

The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections be…

We study existence, uniqueness and regularity of solutions for linear equations in infinitely many derivatives. We develop a natural framework based …

We now extend our analysis to the upper thresholds. We will show that if λq0 is an eigenvalue of multiplicity m0≥1 of (−Δω), then m0 is a bound for the number of resonances around λq0.

We consider the Dirichlet Laplacian in a straight three dimensional waveguide with non-rotationally invariant cross section, perturbed by a twisting …

In this paper we present a phantom solution with a big rip singularity in a non-linear regime of the Israel-Stewart formalism. In this framework it i…

Let $S=R\cup B$ be a point set in the plane in general position such that each of its elements is colored either red or blue, where $R$ and $B$ denot…

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