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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.
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tom 10
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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 Three methods for the study of semilinear equations at resonance
100%
Przeradzki B.
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tom 66
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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.
3
Content available remote A note on solutions of semilinear equations at resonance in a cone
100%
Przeradzki B.
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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]).
4
Content available remote A topological version of the Ambrosetti-Prodi theorem
100%
Przeradzki B.
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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.
5
Content available remote Wave fronts to some modifications of Korteweg-de Vries and Burgers-Korteweg-de Vries equations
63%
Przeradzki B. , Szymańska-Dębowska K.
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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.
6
Content available remote On the homotopical classification of DJ-mappings of infnitely dimensional spheres
50%
Przeradzki B.
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nr 2
143-149
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