On the Nagumo uniqueness theorem

By a convenient reparametrisation of the integral curves of a nonlinear ordinary differential equation (ODE), we are able to improve the conclusions of the recent contribution [A. Constantin, Proc. Japan Acad. {\bf 86(A)} (2010), 41--44]. In this way, we establish a flexible uniqueness criterion for ODEs without Lipschitz-like nonlinearities

Coincidences for Admissible and Φ★Maps and Minimax Inequalities

AbstractA coincidence theory for Φ★and admissible maps is presented in this paper. One can also deduce from this theory new minimax inequalities of von Neumann–Sion type

Solvability of some fourth (and higher) order singular boundary value problems

AbstractExistence results for a variety of singular fourth order boundary value problems of the form yiv = f(t, y, y′, y″) are given. Here our nonlinear term f may be singular at t = 0, t = 1, y = 0, and/or y″ = 0. For example, some singularities of the type y−a and ¦y″¦−b are included. Also we discuss and treat the extension of these results to nth order boundary value problems

Quotient probabilistic normed spaces and completeness results

We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.Comment: 10 page

On a fractional differential equation with infinitely many solutions

We present a set of restrictions on the fractional differential equation $x^{(\alpha)}(t)=g(x(t))$, $t\geq0$, where $\alpha\in(0,1)$ and $g(0)=0$, that leads to the existence of an infinity of solutions starting from $x(0)=0$. The operator $x^{(\alpha)}$ is the Caputo differential operator

Positive Solutions of Singular and Nonsingular Fredholm Integral Equations

AbstractThe existence of positive solutions of the Fredholm nonlinear equation y(t)=h(t)+∫T0k(t,s)[f(y(s))+g(y(s))]ds is discussed. It is assumed that f is a continuous, nondecreasing function and g is continuous, nonincreasing, and possibly singular