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1
Content available remote

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

100%
Przeradzki B.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2012-2018
EN
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.
2
Content available remote

A note on solutions of semilinear equations at resonance in a cone

100%
Przeradzki B.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 1
95-103
EN
A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).
3
Content available remote

A topological version of the Ambrosetti-Prodi theorem

100%
Przeradzki B.
Annales Polonici Mathematici
|
1996
|
tom 64
|
nr 2
121-130
EN
The existence of at least two solutions for nonlinear equations close to semilinear equations at resonance is obtained by the degree theory methods. The same equations have no solutions if one slightly changes the right-hand side. The abstract result is applied to boundary value problems with specific nonlinearities.
4
Content available remote

Three methods for the study of semilinear equations at resonance

100%
Przeradzki B.
Colloquium Mathematicum
|
1993
|
tom 66
|
nr 1
109-12
EN
Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method [22]-[27]. Some extension of the last method and applications to differential equations in Banach spaces are presented.
5
Content available remote

Positive solutions for sublinear elliptic equations

64%
Przeradzki B., Stańczy R.
Colloquium Mathematicum
|
2002
|
tom 92
|
nr 1
141-151
EN
The existence of a positive radial solution for a sublinear elliptic boundary value problem in an exterior domain is proved, by the use of a cone compression fixed point theorem. The existence of a nonradial, positive solution for the corresponding nonradial problem is obtained by the sub- and supersolution method, under an additional monotonicity assumption.
6
Content available remote

Wave fronts to some modifications of Korteweg-de Vries and Burgers-Korteweg-de Vries equations

64%
Przeradzki B., Szymańska-Dębowska K.
Banach Center Publications
|
2014
|
tom 101
|
nr 1
163-168
EN
The existence of a traveling wave with special properties to modified KdV and BKdV equations is proved. Nonlinear terms in the equations are defined by means of a function f of an unknown u satisfying some conditions.
7
Content available remote

A nonlocal elliptic equation in a bounded domain

51%
Fijałkowski P., Przeradzki B., Stańczy R.
Banach Center Publications
|
2004
|
tom 66
|
nr 1
127-133
EN
The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form $-∑_{i,j=1}^{n} D_i(a_{ij}D_ju) = f(u,∫_{Ω}g(u^p))$, in a bounded domain Ω in ℝⁿ with some growth assumptions on the nonlinear terms f and g is proved. The method based on the Krasnosel'skiĭ Fixed Point Theorem enables us to find many solutions as well.
8
Content available remote

On the homotopical classification of DJ-mappings of infnitely dimensional spheres

50%
Przeradzki B.
Fundamenta Mathematicae
|
1984
|
tom 120
|
nr 2
143-149
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