Related papers: General solutions for some classes of interacting …

A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…

Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…

This work deals with defect structures in models described by scalar fields. The investigations focus on generalized models, with the kinetic term modified to allow for a diversity of possibilities. We develop a new framework, in which we…

The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of solution is given, by recasting the…

We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…

We study an example of higher-order field-theoretic model with an eighth-degree polynomial potential -- the $\varphi^8$ model. We show that for some certain ratios of constants of the potential, the problem of finding kink-type solutions in…

In this paper all the defect-type solutions in a family of scalar field theories with a real and a complex field in (1+1) dimensional Minkowski spacetime have been analytically identified. Three types of solutions have been found: (a)…

We present a general procedure to solve the equations of motion for cosmological models driven by real scalar fields with first-order differential equations. The method seems to have great power, since it works for closed, flat or open…

In this paper, we consider a class of fully nonlinear equations on closed smooth Riemannian manifolds, which can be viewed as an extension of $\sigma_k$ Yamabe equation. Moreover, we prove local gradient and second derivative estimates for…

We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…

We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of…

In this paper, we study the solvability of a general class of fully nonlinear curvature equations, which can be viewed as generalizations of the equations for Christoffel-Minkowski problem in convex geometry. We will also study the…

The main point of this paper is to present a class of equations over integers that one can check if they have a solution by checking a set of inequalities. The prototype of such equations is the equations appearing in the well-known…

A class of exact solutions is obtained for the Li\'{e}nard type ordinary non-linear differential equation. As a first step in our study the second order Li\'{e}nard type equation is transformed into a second kind Abel type first order…

The present work investigates several models of a single real scalar field, engendering kinetic term of the Dirac-Born-Infeld type. Such theories introduce nonlinearities to the kinetic part of the Lagrangian, which presents a square root…

We present some results on a fully nonlinear version of the Yamabe problem and a Harnack type inequality for general conformally invariant fully nonlinear second order elliptic equations.

Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…

We prove a general theorem on the existence of heteroclinic orbits in Hilbert spaces, and present a method to reduce the solutions of some P.D.E. problems to such orbits. In our first application, we give a new proof in a slightly more…

The Riccati equation method is used to establish some global solvability criteria for some classes of second order nonlinear ordinary differential equations. Two oscillation theorems are proved. The results are applied to the Emden - Fowler…

I shortly describe semi-classical models of spinning electron and list a number of theoretical issues where these models turn out to be useful, see arXiv:1710.07135 for details. Then I discuss the possibility to extend the range of…