Related papers: Uniqueness of a Negative Mode About a Bounce Solut…
We study perturbations of the eigenvalue problem for the negative Laplacian plus an indefinite and unbounded potential and Robin boundary condition. First we consider the case of a sublinear perturbation and then of a superlinear…
In this paper we cover a few topics on how to treat inverse problems. There are two different flows of ideas. One approach is based on Morse Lemma. The other is based on analyticity which proves that the number of solutions to the inverse…
We propose a family of dilaton gravity models possessing bouncing solutions with interiors connecting separate asymptotically flat regions. We demonstrate that inner Cauchy horizons are stable given certain initial conditions. We study…
We investigate the bounce solutions in vacuum decay problems. We show that it is possible to have a stable false vacuum in a potential that is unbounded from below.
We address the equilibrium concept of a reverse auction game so that no one can enhance the individual payoff by a unilateral change when all the others follow a certain strategy. In this approach the combinatorial possibilities to consider…
We offer a new proposal for cosmic singularity resolution based upon a quantum cosmology with a unitary bounce. This proposal is illustrated via a novel quantization of a mini-superspace model in which there can be superpositions of the…
In his 1977 paper on vacuum decay in field theory: The Fate of the False Vacuum, Coleman considered the problem of a single scalar field and assumed that the minimum action tunnelling field configuration, the bounce, is invariant under O(4)…
We study the effects of internal symmetries on the decay by bubble nucleation of a metastable false vacuum. The zero modes about the bounce solution that are associated with the breaking of continuous internal symmetries result in an…
In this study, the source of the black bounce is discussed in the context of $f(Q)$ theory. A body of research has been dedicated to the study of symmetric black bounce solutions that are generated by a combination of a scalar field with a…
We extend the previous work about the cosmological solutions with bounce without modifications of gravity or introducing an extra scalar field. The main finding was that the bounce is possible in the initially contracting Universe filled…
This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the unique recovery of sound-soft obstacles with a smooth boundary…
We study some properties of the obstacle reactions associated with the solutions of unilateral obstacle problems with measure data. These results allow us to prove that, under very weak assumptions on the obstacles, the solutions do not…
This paper provides a direct method of establishing the existence and uniqueness of saddle-node bifurcations for nonlinear equations in general domains. The method employs the scaled extended quotient whose saddle points correspond to the…
By using a specially constructed cone and the fixed point index theory, this paper investigates the existence of multiple positive solutions for the third-order three-point singular semipositone BVP: $\begin{cases} x'''(t)-\ld f(t,x) =0,…
We show that the system of Gaudin's equations for quasimomenta k_{j}, which describes a one-dimensional system of spinless point bosons with zero boundary conditions, has the unique real solution for each set of quantum numbers n_{j}.
We consider the inverse boundary value problem for the steady state convection diffusion equation. We prove that a velocity field $V$, is uniquely determined by the Dirichlet-to-Neumann map, when $V \in C^{0,\gamma} (\Omega)$, $2/3< \gamma…
We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced…
This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear fractional differential equation with mixed boundary value conditions. Riemann-Liouville fractional derivative is considered. An…
For a singular Liouville equation, it is plausible that a non-simple blowup phenomenon occurs around a quantized singular pole. The presence of complex blowup profiles of bubbling solutions presents substantial challenges in applications.…
In the standard procedure for calculating the decay rate of a metastable vacuum the solution of the classical Euclidean equation of motion of the background field is needed. On the other hand radiative corrections have to be taken into…