Related papers: Fractional Klein-Gordon equation with singular mas…
We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small…
By a bifurcation argument we prove that the capillary-gravity Whitham equation features asymmetrical periodic travelling wave solution of arbitrarily small amplitude. Such waves exist only in the weak surface tension regime…
This paper is concerned with an elliptic system of Kirchhoff type, driven by the variable-order fractional $p(x)$-operator. With the help of the direct variational method and Ekeland variational principle, we show the existence of a weak…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
This paper studies the parabolic $p$-Laplace equation with $p>2$ in a moving domain under a Neumann type boundary condition corresponding to the total mass conservation. We establish the existence and uniqueness of a weak solution by the…
We seek to introduce a mathematical method to derive the Klein-Gordon equation and a set of relevant laws strictly, which combines the relativistic wave functions in two inertial frames of reference. If we define the stationary state wave…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
Schrodinger equation with two-component wave function which describes a relativistic spin 1/2 particle in a weak electromagnetic field is obtained. In the same approximation Schrodinger equation with traditional norm condition and…
In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we…
We study a time fractional heat equation in a noncylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation.
This work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the…
In this study, we discuss an approximate set of equations describing water wave propagating in deep water. These generalized Klein-Gordon (gKG) equations possess a variational formulation, as well as a canonical Hamiltonian and…
In this paper, the space-fractional Schr\"{o}dinger equations with singular potentials are studied. Delta-like or even higher-order singularities are allowed. By using the regularising techniques, we introduce a family of 'weakened'…
The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this note we consider such a problem for the hyperbolic Klein-Gordon equation on Lorentzian manifolds. The investigation could help to…
We consider a relaxation of the viscous Cahn-Hilliard equation induced by the second-order inertial term~$u_{tt}$. The equation also contains a semilinear term $f(u)$ of "singular" type. Namely, the function $f$ is defined only on a bounded…
In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying…
The radial part of the effective mass Klein-Gordon equation for the Hulthen potential is solved by making an approximation to the centrifugal potential. The Nikiforov-Uvarov method is used in the calculations. Energy spectra and the…
We consider a nonlinear Klein--Gordon equation in the nonrelativistic limit regime with highly oscillatory initial data in the form of a modulated plane wave. In this regime, the solution exhibits rapid oscillations in both time and space,…
We introduce $q$-versions of the Klein-Gordon equation in the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to our $q$-deformed Klein-Gordon equations. We show that these plane wave solutions form a…
We consider a class of nonlinear Klein-Gordon equations $u_{tt}=u_{xx}-u+f(u)$ and obtain a family of small amplitude periodic solutions, where the temporal and spatial period have different scales.