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Unique solvability of certain nonlinear boundary value problems via a global inversion theorem of Hadamard-Levy type

Trif T.

Demonstratio Mathematica

2005

Vol. 38, nr 2

331--340

The paper deals with the nonlinear even-order boundary value problem u(2n)(x)=f(x, u(x)), x is an element of [0,l], u(2k)(0)=u(2k)(1)=0, 0

On the superstability of certain function equations

Trif T.

Demonstratio Mathematica

2002

Vol. 35, nr 4

813-820

We prove new results concerning the superstability of the equation (2) (both in the conventional sense and in the sense of R. Ger) and of the equation (3) (in the conventional sense). Likewise, we provide new simple proofs for stronger versions of already known results on the superstability of the equation (1) (both in the conventional sense and in the sense of R. Ger) and of the equation (3) (in the sense of R. Ger).

Positive solutions of a nonlinear integral equation from biomathematics

Trif T.

Demonstratio Mathematica

1999

Vol. 32, nr 1

129-138

The aim of the present paper is to investigate the existence of positive continuous solutions of the nonlinear integral equation x(t) = St-r f(s, x(s))ds, arising in infectious diseases. We give sufficient conditions ensuring the existence of positive periodic continuous solutions of this equation, provided that f is a continuous function periodic in the first argument. We also study the existence of positive continuous solutions of the initial value problem for the considered equation.