Slawomir M. Rybicki Nicolaus Copernicus University (Poland)
Global bifurcations of solutions of elliptic systems
The aim of my talk is to present Rabinowitz alternative for systems of elliptic differential equations of the
form
where
 Ω ⊂ R^{N} is an open, bounded subset of R^{N}, with boundary of the class C^{1},
 F C^{2}(R^{m} × R,R),
 dsF(x,λ) = ⟨Ax,x⟩ + η(x,λ), where
 A is a symmetric (m × m)matrix,
 ∇_{x}η(0,λ) = 0, for any λ R,
 ∇_{x}^{2}η(0,λ) = 0, for any λ R,
 there are C > 0 and 1 ≤ p < (N + 2)(N  2)^{1} such that for any (x,λ) R^{n} ×R the following inequality
holds true ∇_{x}F(x,λ)≤ C.
