Wyniki wyszukiwania

1

The Conley index in Hilbert spaces and its applications

100%

Gęba K., Izydorek M., Pruszko A.

Studia Mathematica

|

1999

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tom 134

|

nr 3

217-233

EN

We present a generalization of the classical Conley index defined for flows on locally compact spaces to flows on an infinite-dimensional real Hilbert space H generated by vector fields of the form f: H → H, f(x) = Lx + K(x), where L: H → H is a bounded linear operator satisfying some technical assumptions and K is a completely continuous perturbation. Simple examples are presented to show how this new invariant can be applied in searching critical points of strongly indefinite functionals having asymptotically linear gradient.

2

Classification of homotopy classes of equivariant gradient maps

100%

Dancer E., Gęba K., Rybicki S.

Fundamenta Mathematicae

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2005

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tom 185

|

nr 1

1-18

EN

Let V be an orthogonal representation of a compact Lie group G and let S(V),D(V) be the unit sphere and disc of V, respectively. If F: V → ℝ is a G-invariant C¹-map then the G-equivariant gradient C⁰-map ∇F: V → V is said to be admissible provided that $(∇F)^{-1}(0) ∩ S(V) = ∅$. We classify the homotopy classes of admissible G-equivariant gradient maps ∇F: (D(V),S(V)) → (V,V∖{0}).

3

Spaces of continuous functions (V) (On linear isotonical embedding of $C(Ω_{1})$ into $C(Ω_{2})$)

87%

Gęba K., Semadeni Z.

Studia Mathematica

|

1960

|

tom 19

|

nr 3

303-320

4

Algebraic topology methods in the theory of compact fields in Banach spaces

74%

Gęba K.

Fundamenta Mathematicae

|

1964

|

tom 54

|

nr 2

177-209

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Studia Mathematica

4 Gęba K.

1 Dancer E.

1 Izydorek M.

1 Pruszko A.

1 Rybicki S.

1 Semadeni Z.

1 2005

1 1999

1 1964

1 1960

The Conley index in Hilbert spaces and its applications

Classification of homotopy classes of equivariant gradient maps

Spaces of continuous functions (V) (On linear isotonical embedding of $C(Ω_{1})$ into $C(Ω_{2})$)

Algebraic topology methods in the theory of compact fields in Banach spaces