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We prove that the fractional Yamabe equation ${\rm {\cal L}}_\gamma u = \vert u \vert ^{((4\gamma)/(Q-2\gamma))}u$ on the Heisenberg group ℍ n has [ n + 1/2] sequences of nodal (sign-changing) weak solutions whose elements have mutually different nodal properties, where ${\rm {\cal L}}_\gamma $ denotes the CR fractional sub-Laplacian operator on ℍ n , Q = 2 n + 2 is the homogeneous dimension of ℍ n , and $\gamma \in \bigcup\nolimits_{k = 1}^n [k,((kQ)/Q-1)))$. Our argument is variational, based on a Ding-type conformal pulling-back transformation of the original problem into a problem on the CR sphere S 2 n + 1 combined with a suitable Hebey-Vaugon-type compactness result and group-theoretical constructions for special subgroups of the unitary group U (n + 1). [ABSTRACT FROM AUTHOR]

The Triassic-Jurassic boundary (TJB) is marked by one of the five largest Phanerozoic mass extinctions. To constrain existing models for TJB events, we obtained a stratigraphically highly resolved dataset from a marine section at Kendlbachgraben, Austria.The topmost Triassic Kössen Formation contains low to medium-charged smectite and vermiculite as alteration products of mafic-ultramafic minerals. The clay minerals in the boundary mudstone are kaolinite 5 illite + muscovite >> smectite > chlorite. Predominant kaolinite suggests humid climate and abundant terrigenous input. In the lowermost Jurassic, the clay mineral pattern changes to illite + muscovite >> kaolinite >> smectite, which reflects change to less humid and more moderate climate.The topmost Kössen Formation also contains clay spherules. Their composition, shape and size indicate that they are alteration products of airborne volcanic glass droplets solidified in the air, settled in the sea and altered rapidly with negligible transport in terrestrial or marine environments. Our data are consistent with sudden climatic change at the TJB, as a result of large-scale volcanic activity of the Central Atlantic Magmatic Province which produced distal airfall volcanic ash. [ABSTRACT FROM AUTHOR]

If Ω is an unbounded domain in ℝN and p > N, the Sobolev space W1,p(Ω) is not compactly embedded into L∈(Ω). Nevertheless, we prove that if Ω is a strip-like domain, then the subspace of W1,p(Ω) consisting of the cylindrically symmetric functions is compactly embedded into L∈(Ω). As an application, we study a Neumann problem involving the p-Laplacian operator and an oscillating nonlinearity, proving the existence of infinitely many weak solutions. Analogous results are obtained for the case of partial symmetry. [ABSTRACT FROM PUBLISHER]

In this paper we study a non-homogeneous Neumann-type problem which involves a nonlinearity satisfying a non-standard growth condition. By using a recent variational principle of Ricceri, we establish the existence of at least two non-trivial solutions in an appropriate Orlicz–Sobolev space. [ABSTRACT FROM PUBLISHER]

In this paper we solve partially an open problem raised by B. Ricceri (Bull. London Math. Soc.33 (2001), 331–340). Infinitely many solutions for a Neumann problem are obtained through a direct variational approach where the nonlinearity has an oscillatory behaviour at infinity. [ABSTRACT FROM PUBLISHER]