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1
Content available remote

Stationary solutions of the generalized Smoluchowski-Poisson equation

100%
Stańczy R.
Banach Center Publications
|
2008
|
tom 81
|
nr 1
493-500
EN
The existence of steady states in the microcanonical case for a system describing the interaction of gravitationally attracting particles with a self-similar pressure term is proved. The system generalizes the Smoluchowski-Poisson equation. The presented theory covers the case of the model with diffusion that obeys the Fermi-Dirac statistic.
2
Content available remote

On radially symmetric solutions of some chemotaxis system

100%
Stańczy R.
Banach Center Publications
|
2009
|
tom 86
|
nr 1
303-312
EN
This paper contains some results concerning self-similar radial solutions for some system of chemotaxis. This kind of solutions describe asymptotic profiles of arbitrary solutions with small mass. Our approach is based on a fixed point analysis for an appropriate integral operator acting on a suitably defined convex subset of some cone in the space of bounded and continuous functions.
3
Content available remote

Hammerstein equations with an integral over a noncompact domain

100%
Stańczy R.
Annales Polonici Mathematici
|
1998
|
tom 69
|
nr 1
49-60
EN
The existence of solutions of Hammerstein equations in the space of bounded and continuous functions is proved. It is obtained by the Schauder fixed point theorem using a compactness theorem. The result is applied to Wiener-Hopf equations and to ODE's.
4
Content available remote

On some parabolic-elliptic system with self-similar pressure term

100%
Stańczy R.
Banach Center Publications
|
2006
|
tom 74
|
nr 1
205-215
EN
A priori estimates for solutions of a system describing the interaction of gravitationally attracting particles with a self-similar pressure term are proved. The presented theory covers the case of the model with diffusions that obey either Fermi-Dirac statistics or a polytropic one.
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

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.
7
Content available remote

Nonisothermal systems of self-attracting Fermi-Dirac particles

51%
Biler P., Nadzieja T., Stańczy R.
Banach Center Publications
|
2004
|
tom 66
|
nr 1
61-78
EN
The existence of stationary solutions and blow up of solutions for a system describing the interaction of gravitationally attracting particles that obey the Fermi-Dirac statistics are studied.
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