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Note on weakly inward mappings

100%
Fečkan M.
Annales Polonici Mathematici
|
1996
|
tom 63
|
nr 1
1-5
EN
The Nielsen fixed point theory is used to show several results for certain operator equations involving weakly inward mappings.
2
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The interaction of linear boundary value and nonlinear functional conditions

100%
Fečkan M.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 3
299-310
EN
The existence of solutions is studied for certain nonlinear differential equations with both linear and nonlinear conditions
3
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Nontrivial critical points of asymptotically quadratic functions at resonances

100%
Fečkan M.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 1
43-57
EN
Asymptotically quadratic functions defined on Hilbert spaces are studied by using some results of the theory of Morse-Conley index. Applications are given to existence of nontrivial weak solutions for asymptotically linear elliptic partial and ordinary differential equations at resonances.
4
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Critical points of asymptotically quadratic functions

100%
Fečkan M.
Annales Polonici Mathematici
|
1995
|
tom 61
|
nr 1
63-76
EN
Existence results for critical points of asymptotically quadratic functions defined on Hilbert spaces are studied by using Morse-Conley index and pseudomonotone mappings. Applications to differential equations are given.
5
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Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses

51%
Fečkan M., Wang J., Zhou Y.
Nonautonomous Dynamical Systems
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2014
|
tom 1
|
nr 1
EN
In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem. Furthermore, existence of a global compact connected attractor for the Poincaré operator is derived.
6
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On the nonlocal Cauchy problem for semilinear fractional order evolution equations

51%
Wang J., Zhou Y., Fečkan M.
Open Mathematics
|
2014
|
tom 12
|
nr 6
911-922
EN
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first result relies on a growth condition on the whole time interval via Schaefer fixed point theorem. The second result relies on a growth condition splitted into two parts, one for the subinterval containing the points associated with the nonlocal conditions, and the other for the rest of the interval via O’Regan fixed point theorem.
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