Functional-topological properties of the Plateau operator and applications to the study of bifurcations in problems of geometry and hydrodynamics

Parameterized splitting theorems and bifurcations for potential operators, Part II: Applications to quasi-linear elliptic equations and systems

“…x u yy ) = λu, u| ∂Ω = 0, (4.27) which was studied in [6,7] with functional-topological properties of the Plateau operator. When ∂Ω is of class C 2,1 , n = 2, k = 3 and p > 2 our results are supplement for [6,7].…”

“…It is possible that results in this paper are generalized to the case of unbounded domains Ω ⊂ R n with [41]. We believe that theories in this series can also be used to improve bifurcation results for geometric variational problems such as [6] and [4,3], etc., see [27]. Other applications will be given in [24,25,26].…”

“…Corollaries A.7, A.8 of the main result Theorem A. 6 were only stated and used in case m = 2 in [42]. In Appendix B we prove three lemmas, which fill in the detail on much of the proof of Theorem 3.10.…”

Buckling and postcritical behaviour of the elastic infinite plate strip resting on linear elastic foundation

“…The CrandallRabinowitz theorem in the gradient case will be used as the sufficient condition of bifurcation (see [6,7,11,34]). Theorem 5.1 (see [11] or [6]). In Banach spaces X , Y let us consider equation…”

“…which is simple in verification (see, for example, [6,7]). Basing on Remark 1.2 it is known, that in problem (1.1) there can be subcritical bifurcation (Fig.…”