14 papers
Geometrically distinct unbounded continua of solutions for Yamabe-type equations
Piotr Stefaniak
We study global bifurcation for Yamabe-type equations on closed Riemannian manifolds with symmetries. For isometric group actions with interval orbit space and a suitable range of…
Periodic solutions of autonomous -symmetric Newtonian systems
A. Golebiewska, S. Rybicki, P. Stefaniak
The aim of this paper is to formulate necessary conditions and sufficient ones for the existence of closed connected sets of nonstationary -periodic solutions of -symmetr…
Global bifurcation of solutions to elliptic systems with system and domain symmetries
Piotr Stefaniak
We study parameterized elliptic systems on symmetric domains with additional system symmetries. We prove the existence of continua of nontrivial solutions bifurcating from the cons…
Wavelet based solutions to the Poisson and the Helmholtz equations on the -dimensional unit sphere
Ilona Iglewska-Nowak, Piotr Stefaniak
We present a method of solving partial differential equations on the -dimensional unit sphere using methods based on the continuous wavelet transform derived from approximate id…
Unbounded sets of solutions of non-cooperative elliptic systems on symmetric spaces
Piotr Stefaniak
The aim of this paper is to show that, for a class of non-cooperative elliptic systems on compact symmetric spaces, any continuum of nontrivial solutions bifurcating from the set o…
Periodic solutions to symmetric Newtonian systems in neighborhoods of orbits of equilibria
Anna Gołębiewska, Marta Kowalczyk, Sławomir Rybicki +1
The aim of this paper is to prove the existence of periodic solutions to symmetric Newtonian systems in any neighborhood of an isolated orbit of equilibria. Applying equivariant bi…
Wavelet methods in partial differential equations on spheres
{Ilona Iglewska-Nowak, Piotr Stefaniak
We propose a method of solving partial differential equations on the -dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate i…
Bifurcations from degenerate orbits of solutions of nonlinear elliptic systems
Anna Gołębiewska, Joanna Kluczenko, Piotr Stefaniak
The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball.…
Structure of sets of solutions of parametrised semi-linear elliptic systems on spheres
Anna Gołębiewska, Piotr Stefaniak
In this paper we study a parametrised non-cooperative symmetric semi-linear elliptic system on a sphere. Assuming that there exist critical orbits of the potential, we study the st…
Connected sets of solutions of symmetric elliptic systems
Anna Gołębiewska, Sławomir Rybicki, Piotr Stefaniak
The purpose of this paper is twofold. First we study bifurcations of connected sets of critical orbits of some invariant functional from a given family of critical orbits. We use t…
Global bifurcation index of critical orbit of strongly indefinite functional
Anna Gołębiewska, Piotr Stefaniak
In this paper we study an index of a critical orbit, defined in terms of the degree for invariant strongly indefinite functionals. We establish a relationship of this index with th…
Bifurcations from the orbit of solutions of the Neumann problem
Anna Gołębiewska, Joanna Kluczenko, Piotr Stefaniak
The purpose of this paper is to study weak solutions of a nonlinear Neumann problem considered on a ball. Assuming that the potential is invariant, we consider an orbit of critical…
Rabinowitz alternative for non-cooperative elliptic systems on geodesic balls
Sławomir Rybicki, Naoki Shioji, Piotr Stefaniak
The purpose of this paper is to study properties of continua (closed connected sets) of nontrivial solutions of non-cooperative elliptic systems considered on geodesic balls in $S^…
Symmetry breaking of solutions of non-cooperative elliptic systems
Piotr Stefaniak
In this article we study the symmetry breaking phenomenon of solutions of noncooperative elliptic systems. We apply the degree for G-invariant strongly indefinite functionals to ob…