Badania

Badania prowadzone w katedrze związane są z:

• Zagadnieniami brzegowymi eliptycznymi w obszarach niegładkich.
• Teorią systemów wyznacznikowych i operatorów Fredholma.
• Analizą nieliniową.
• Współzmienniczą analizą nieliniową.
• Wariacyjnymi metodami w analizie nieliniowej.
• Teorią bifurkacji.
• Teorią ergodyczną i topologicznymi układami dynamicznymi.
• Układami dynamicznymi, geometrią różniczkową i fizyką matematyczną.
• Modelowaniem matematycznym w biologii i medycynie.

W Katedrze prowadzone są dwa seminaria naukowe:

• Seminarium Eliptyczne Zagadnienia Brzegowe
• Seminarium Układy Dynamiczne i Geometria

Wykaz monografii naukowych:

• M. Borsuk, W. Kondratiev, Elliptic boundary value problems of second order in piecewise smooth domains, ELSEVIER, North-Holland Mathematical Libfrary, Vol. 69 (2006), 531 stron.
• M. Borsuk, Degenerate elliptic boundary-value problems of second order in nonsmooth domains, Journal of Mathematical Sciences, Vol. 146, no. 5 (2007), pp. 6071 – 6212.
• M. Borsuk, Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains, A Springer Basel book Series: Frontiers in Mathematics, 1st Edition, 2010, XII, 220 stron.

Wykaz ważniejszych publikacji naukowych:

• M. Bodzioch, M. Borsuk, Behavior of strong solutions to the degenerate oblique derivative problem for elliptic quasi-linear equations in a neighborhood of a boundary conical point, Complex Variables and Elliptic Equations, Vol. 60 (2015), no. 4, pp. 510-528.
• M. Bodzioch, M. Borsuk, The degenerate second-order elliptic oblique derivative problem in a domain with conical boundary point, Current Trends in Analysis and Its Applications, Trends in Mathematics 2015, pp. 11-18.
• M. Bodzioch, M. Borsuk, On the degenerate oblique derivative problem for elliptic second-order equation in a domain with boundary conical point, Complex Variables and Elliptic Equations, Vol. 59 (2014), No. 3, pp. 324–354.
• M. Borsuk, A priori estimates and solvability of second order quasilinear elliptic equations in a composite domain with nonlinear boundary conditions and conjunction condition, Proc. Steklov Inst. of Math. Vol. 103, (1970), p. 13-51.
• M. Borsuk, Best-possible estimates of solutions of the Dirichlet problem for second order linear elliptic nondivergence equations in the neighborhood of a conical boundary point, Math. USSR Sbornik. Vol. 74, No. 1 (1993), pp. 185-201.
• M. Borsuk, Estimates of generalized solutions to the Dirichlet problem for second-order quasilinear elliptic equations in a domain with a conic point on the boundary, Differential equations, Vol. 31, No. 6 (1995), pp. 936-941.
• M. Borsuk, Dini continuity of the first derivatives of genera lized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains, Ann. Polon. Math. Vol. 69, No. 2 (1998), pp. 129-154. // Siberian. Math. J. Vol. 39, No. 2 (1998), pp. 226-244.
• M. Borsuk, The behavior of solutions of elliptic quasilinear degenerate equations near a boundary edge, Nonlinear Analysis: Theory, Methods & Applications, Vol. 56, No. 3 (2004), pp. 347–384.
• M. Borsuk, The transmission problem for quasi-linear elliptic second order equations in a conical domain: I, II, Nonlinear Analysis: Theory, Methods and Applications, Vol. 71, No. 10 (2009), pp. 5032–5083.
• M. Borsuk, The behavior near the boundary corner point of solutions to the degenerate oblique derivative problem for elliptic second-order equations in a plane domain, Journal of Differential Equations, Vol. 254 (2013), pp. 1601–1625.
• M. Borsuk, D. Wiśniewski, Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains, Central European Journal of Mathematics, Vol. 10, No. 6 (2012), pp. 2051–2072.
• M. Borsuk, A. Zawadzka, Best possible estimates of solutions to the Robin boundary value problem for linear elliptic non divergence second order equations in a neighborhood of the conical point, Journal of Differential Equations, Vol. 207, No. 2 (2004), pp. 303–359.
• M. Borsuk, K. Żyjewski, Nonlocal Robin problem for elliptic second order equations in a plane domain with a boundary corner point, Applicationes Mathematicae, Vol. 38, No. 4 (2011), pp. 369–411.
• M. Borsuk, K. Żyjewski, Nonlocal Robin problem for elliptic quasi-linear second order equations, Advanced nonlinear studies, Vol. 14 (2014), pp. 159-182.
• G. Ciecierska, Cauchy-Binet type formulas for Fredholm operators, Journal of Applied Mathematics and Computational Mechanics, 2 no. 16 (2017), pp. 43--54.
• G. Ciecierska, Determinant systems method for computing reflexive generalized inverses of products of Fredholm operators, Mathematica Aeterna, 6 no. 6 (2016), pp. 895 - 906.
• G. Ciecierska, An application of Plemelj-Smithies formulas to computing generalized inverses of Fredholm operators, Journal of Applied Mathematics and Computational Mechanics, 1 no. 14 (2015), pp. 13--26.
• G. Ciecierska, Formulas of Fredholm type for Fredholm linear equations in Frechet spaces, Mathematica Aeterna, 5 no. 5 (2015), 945-960.
• G. Ciecierska, Determinant systems for nuclear perturbations of Fredholm operators in Frechet spaces, International Publications USA, PanAmerican Mathematical Journal, 24 no. 1 (2014), pp. 1--20.
• G. Ciecierska, On some application of algebraic quasinuclei to the determinant theory, Journal of Applied Mathematics and Computational Mechanics, 3 no. 12 (2013), pp. 27-38.
• G. Ciecierska, On some property of the modified power of an algebraic nucleus, Scientific Research of the Institute of Mathematics and Computer Science, 2 no. 7 (2008), pp. 15-21.
• G. Ciecierska, A note on another method of computing the Moore-Penrose inverse of a matrix, Demonstratio Mathematica,  31 no. 4 (1998), pp. 879-886.
• G. Ciecierska, Analytic formulae for determinant systems for a certain class of Fredholm operators in Banach spaces, Demonstratio Mathematica,  (30) no. 2, (1997)  pp. 387-402.
• J.Gawrycka, S. Rybicki, Solutions of systems of elliptic differential equations on circular domains, Nonlinear Analysis 59 (2004) 1347 - 1367.
• J.Gawrycka, S. Rybicki, Solutions of multiparameter systems
  of elliptic differential equations, Advanced Nonlinear Studies 5 (2005) 279 - 302.
• J. Kluczenko, Bifurcation and symmetry breaking of solutions of systems of elliptic differential equations, Nonlinear Anal.75 (2012), no.11, 4278 - 4295.
• J. Kluczenko, Multiparameter bifurcation and symmetry breaking of solutions elliptic differential equations, Advanced in Differential Equations (20) 2015, no.5-6,531-556
• D. Wiśniewski, Boundary value problems for a second-order elliptic equation in unbounded domains, Ann, Univ. Paedag. Cracov., Studia Math., IX (2010), 87-122
• D. Wiśniewski, The behaviour of weak solutions of boundary value problems for linear elliptic second order equations in unbounded cone-like domains, Annales Mathematicae Silesianae (2016), 30, 203-217
• D. Wiśniewski, M. Bodzioch, An integro - differential inequality related to the smallest positive eigenvalue of p(x)-Laplacian Dirichlet problem, Ann.Univ.Paedag. Cracov.Studia Math. (2016), 15, 27-36
• D. Wiśniewski, Best possible estimates of weak solutions of boundary value problems for quasi-linear elliptic divergence equations in unbounded domains, An. St. Math. Series (zaakceptowane 5 lipca 2016)
• K. Żyjewski, Nonlocal Robin problem in a plane domain with a boundary corner point, Annales Universitatis Paedagogicae Cracoviensis, Studia Mathematica, Vol. X (2011), pp. 5-34.

Wykaz ważniejszych publikacji dydaktycznych:

• D. Wiśniewski, Wokół liczb i szeregów harmonicznych, Annales Universitatis Paedagogicae Cracoviensis Studia ad Didacticam Mathematicae Pertinentia, vol. VII, (2015), 99-110
• K. Żyjewski, D. Wiśniewski, Metoda Frobeniusa, czyli o rozwiązywaniu pewnej klasy równań różniczkowych, Annales Universitatis Paedagogicae Cracoviensis Studia ad Didacticam Mathematicae Pertinentia (zaakceptowane 02.03.2017)