Applications of an extended -expansion method to find exact solutions of nonlinear PDEs in mathematical physics.
Applications of the new compound Riccati equations rational expansion method and Fan's subequation method for the Davey-Stewartson equations.
Approximate ad hoc parametric solutions for nonlinear first-order PDEs governing two-dimensional steady vector fields.
Comparison theorems for Riccati inequalities arising in the theory of PDEs with -Laplacian.
Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method.
Forced oscillations of half-linear elliptic equations via Picone-type inequality.
Generalized Picone and Riccati inequalities for half-linear differential operators with arbitrary elliptic matrices.
Hematologic Disorders and Bone Marrow–Peripheral Blood Dynamics
Hematologic disorders such as the myelodysplastic syndromes (MDS) are discussed. The lingering controversies related to various diseases are highlighted. A simple biomathematical model of bone marrow - peripheral blood dynamics in the normal state is proposed and used to investigate cell behavior in normal hematopoiesis from a mathematical viewpoint. Analysis of the steady state and properties of the model are used to make postulations about the...
Lanczos-like algorithm for the time-ordered exponential: The -inverse problem
The time-ordered exponential of a time-dependent matrix is defined as the function of that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in . The authors have recently proposed the first Lanczos-like algorithm capable of evaluating this function. This algorithm relies on inverses of time-dependent functions with respect to a non-commutative convolution-like product, denoted by . Yet, the existence of such inverses, crucial to...
Multiplicity of solutions for a singular p-laplacian elliptic equation
The existence of two continuous solutions for a nonlinear singular elliptic equation with natural growth in the gradient is proved for the Dirichlet problem in the unit ball centered at the origin. The first continuous solution is positive and maximal; it is obtained via the regularization method. The second continuous solution is zero at the origin, and follows by considering the corresponding radial ODE and by sub-sup solutions method.
New method to solve certain differential equations
A new method to solve stationary one-dimensional Schroedinger equation is investigated. Solutions are described by means of representation of circles with multiple winding number. The results are demonstrated using the well-known analytical solutions of the Schroedinger equation.
Nonexistence of radial positive solutions for a nonpositone problem.
Oscillation of solutions for forced nonlinear neutral hyperbolic equations with functional arguments.
Riesz potentials for Korteweg-de Vries solitons and Sturm-Liouville problems.
Some relatively new techniques for nonlinear problems.