Bogdan Przeradzki

Travelling waves for reaction–diffusion equations with time depending nonlinearities

Abstract The existence of travelling wave with given end points for parabolic system of nonlinear equations is proven. The nonlinear term depends also on a·x−ct where x is the multidimensional space variable, t—time, c—the speed of the wave and a—the direction of travel.

Compactness result and its applications in integral equations

Abstract A version of the Arzelà–Ascoli theorem for X being a σ-locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn operators. Two fixed point theorems, for Hammerstein and Urysohn operators, are derived on the basis of Schauder fixed point theorem.

A generalization of Krasnosel’skii fixed point theorem for sums of compact and contractible maps with application

The existence of a fixed point for the sum of a generalized contraction and a compact map on a closed convex bounded set is proved. The result is applied to a kind of nonlinear integral equations.

On a radial positive solution to a nonlocal elliptic equation

The existence of a solution to the Dirichlet boundary value problem for nonlinear Poisson equations with the nonlocal nonlinear term

Existence of Solutions for Higher Order Bvp with Parameters via Critical Point Theory

-\Delta u=f\bigg(u,\int (g\circ u)\bigg),\quad u\vert\partial U=0,

Solvability of a Multi-Point Boundary Value Problem at Resonance

is proved by means of fixed point theorems for increasing compact operators.

The existence of bounded solutions for differential equations in Hilbert spaces

An approximative approach to a generalized theory of the topological mapping degree is presented. Some new wide classes of operators acting in Banach spaces, which include A-proper mappings of Petryshyn, are introduced and studied from the viewpoint of the homotopic properties of the topological degree. The results are applied in some existence aspects of abstract nonlinear equations.

Positive solutions for sublinear elliptic equations

Abstract This paper is concerned with the existence of at least one solution of the nonlinear 2k-th order BVP. We use the Mountain Pass Lemma to get an existence result for the problem, whose linear part depends on several parameters.