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We show that cosmological sudden singularities that respect the energy conditions can occur at finite times in Brans-Dicke and more general scalar-tensor theories of gravity. We construct these explicitly in the Friedmann universes.…
On a bounded smooth domain we study solutions of a semilinear elliptic equation with an exponential nonlinearity and a Hardy potential depending on the distance to the boundary of the domain. We derive global a priori bounds of the…
We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and allows access to a generalized quantum…
We introduce a new class of higgs type complex-valued scalar fields $U$ with Feynman propagator $\sim 1/p^4$ and consider the matching to the traditional fields with propagator $\sim 1/p^2$ in the viewpoint of effective potentials at tree…
In this paper, we obtain some new results about weakly singular integral inequalities. These inequalities are used to discuss the global existence and uniqueness results for fractional differential equations of Riemann-Liouville type. Some…
We argue that the variational calculus leading to Euler's equations and Noether's theorem can be replaced by equivariance and invariance conditions avoiding the action integral. We also speculate about the origin of Lagrangian theories in…
A covariant Hamiltonian formulation generalizing De Donder-Weyl mechanics is constructed with field strengths as velocity fields. Since the teleparallel equivalents to general relativity are quadratic in field strengths, the field-strength…
We revisit Haagerup's enigmatic reduction theorem \cite[Theorems 2.1 \& 3.1]{HJX} showing how that theorem may be extended to general von Neumann algebras $\M$ equipped with an arbitrary faithful normal semifinite weight in a manner which…
In this survey the contemporary results concerning supersymmetries in generalized Schr\"odinger equations are presented. Namely, position dependent mass Sch\"odinger equations are discussed as well as the equations with matrix potentials.…
We revisit the celebrated Hellmann-Feynman theorem (HFT) in the PT invariant non-Hermitian quantum physics framework. We derive a modified version of HFT by changing the definition of inner product and explicitly show that it holds good for…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
We develop a theory of Feynman propagators for the massive Klein--Gordon equation with asymptotically static perturbations. Building on our previous work on the causal propagators, we employ a framework based on propagation of singularities…
The generalized Kuramoto-Sivashinsky equation in the case of the power nonlinearity with arbitrary degree is considered. New exact solutions of this equation are presented.
The Schr\" odinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring…
Torsion arising from fermionic matter in the Einstein-Cartan formulation of general relativity is considered in the context of Robertson-Walker geometries and the early Universe. An ambiguity in the way torsion arising from hot fermionic…
The domain of validity of the higher-order Schrodinger equations is analyzed for harmonic-oscillator and Coulomb potentials as typical examples. Then the Cauchy theory for higher-order Hartree-Fock equations with bounded and Coulomb…
Recently there has been a growing interest in quantum gravity theories with more than four derivatives, including both their quantum and classical aspects. In this work we extend the recent results concerning the non-singularity of the…
We consider second order differential operators with coefficients which are Gaussian random fields. When the covariance becomes singular at short distances then the propagators of the Schr\"odinger equation as well as of the wave equation…
In the recent paper, Ref. 1, the l-waves Schr\"odinger equation for the Cornell's potential is solved in quantum mechanics with a generalized uncertainty principle by following Ref. 2. It is showed here that the approach of Ref. 2 can only…
Modified gravity has attracted much attention over the last few years and remains a potential candidate for dark energy. In particular, the so-called viable f(R) gravity theories, which are able to both recover General Relativity (GR) and…