On the basis of generalization of upper and lower solution method to the singular two point boundary value problems, the existence theorem of solutions for the system, which models a process of magnetic insulation in plasma is proved.

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover n...

A nonlinear degenerate convection-diffusion initial boundary value problem is studied in a bounded domain. A dynamical boundary condition (containing the time derivative of a solution) is prescribed on the one part of the boundary. This models a non-perfect contact on the boundary. Existence and uniqueness of a weak solution in corresponding function spaces is proved using the backward Euler me...

We study the existence of solutions to a class of problems u + f(t, u) = 0, u(0) = u(1) = 0, where f(t, ·) is allowed to be singular at t = 0, t = 1.

An impulsive boundary value problem with nonlinear boundary conditions for a second order ordinary differential equation is studied. In particular, sufficient conditions are provided so that a compression expansion cone theoretic fixed point theorem can be applied to imply the existence of positive solutions. The nonlinear forcing term is assumed to satisfy usual sublinear or superlinear growth...

A partial nonlinear extension of Lax-Richtmyer approximation theory by Aradhana Kumari Adviser: Professor Dennis Sullivan Lax and Richtmyer developed a theory of algorithms for linear initial value problems that guarantees, under certain circumstances, the convergence to numerical solution of initial value problem. The assumptions are first that the difference equations (algorithms) approximate...

The existence and multiplicity results are shown for certain types of problems with nonlinear boundary value conditions.

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...

Nonspherical perturbation theory has been necessary to understand the meaning of radiation in spacetimes generated through fully nonlinear numerical relativity. Recently, perturbation techniques have been found to be successful for the time evolution of initial data found by nonlinear methods. Anticipating that such an approach will prove useful in a variety of problems, we give here both the p...