2019
Том 71
№ 9

All Issues

O’Regan D.

Articles: 2
Article (English)

Existence of global solutions for some classes of integral equations

Agarwal P., Jabeen T., Lupulescu V., O’Regan D.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 130-148

We study the existence of $L^p$ -solutions for a class of Hammerstein integral equations and neutral functional differential equations involving abstract Volterra operators. Using compactness-type conditions, we establish the global existence of solutions. In addition, a global existence result for a class of nonlinear Fredholm functional integral equations involving abstract Volterra equations is given.

Article (English)

Oscillation of certain fourth-order functional differential equations

Agarwal P., Grace S. R., O’Regan D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 3. - pp. 291–313

Some new criteria for the oscillation of fourth-order nonlinear functional differential equations of the form $$\frac{d^2}{dt^2} \left(a(t) \left(\frac{d^2x(t)}{dt^2}\right)^{α} \right) + q(t)f(x[g(t)])=0, \quad α>0,$$ are established.