Archiv der Mathematik最新文献

We give existence results for weak (possibly unbounded) solutions of Dirichlet problems for elliptic equations having degenerate coercivity and a first order term which has quadratic growth with respect to the gradient. The proof is based on the use of test functions having exponential growth.

A base for a permutation group G acting on a set (Omega ) is a sequence (mathcal {B}) of points of (Omega ) such that the pointwise stabiliser (G_{mathcal {B}}) is trivial. The base size of G is the size of a smallest base for G. Extending the results of a recent paper of the author, we prove a 2013 conjecture of Fritzsche, Külshammer, and Reiche. Moreover, we generalise this conjecture and derive an alternative character theoretic formula for the base size of a certain class of permutation groups. As a consequence of our work, a third formula for the base size of the symmetric group of degree n acting on the subsets of ({1,2,dots , n}) is obtained.

We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the complex inversion formula of the Laplace transform to extend known results for Banach space-valued functions and, specifically, for (C_0)-semigroups.

We discuss some properties of the relative Gromov–Witten invariants counting rational curves with maximal contact order at one point. We compute the number of Cayley’s sextactic conics to any smooth plane curve. In particular, we compute the contribution, from double covers of inflectional lines, to a certain degree two relative Gromov–Witten invariant relative to the curve.

In dimension 5, the contact connected sum of Brieskorn contact spheres is, in general, not a Brieskorn contact sphere.

In this note, we prove a conjecture of Fatehizadeh and Yaqubi regarding the arithmetic mean of the first n Fibonacci numbers. More precisely, we show that there are infinitely many positive integers n such that (n mid sum _{i=1}^{n} F_i) and (n+1 mid sum _{i=1}^{n+1} F_i).

In the present paper, we consider the following fractional Schrödinger equations with combined nonlinearities

where (Nge 2), (sin (0,1)), (a>0), (2<q<p<2^{*}_{s}=frac{2N}{N-2s}), and ((-Delta )^s) is the fractional Laplace operator. Under various conditions on (q<p), (a>0), we investigate the existence of ground state normalized solutions by applying variational methods. Moreover, the asymptotic behavior of mountain pass type normalized solutions is also considered. We generalize the corresponding results in Qi and Zou (J Differ Equ 375:172–205, 2023), which concerns nonlinear Schrödinger equations with combined nonlinearities, to fractional nonlinear Schrödinger equations with combined nonlinearities.

Fréchet and Kolmogorov characterized pre-compact sets in Lebesgue spaces. Since then, many characterizations of various function spaces have been developed. Although Morrey spaces are extensions of Lebesgue spaces, characterizing pre-compact sets within Morrey spaces remains open. This paper suggests that certain closed subspaces of Morrey spaces are more manageable compared to the Morrey spaces themselves. It provides a characterization of pre-compactness for subsets in the closure of compactly supported smooth functions in Banach lattices. This finding refines and broadens the characterization of pre-compact subsets in Morrey spaces.

In this paper, we consider the logistic elliptic equation (-Delta u = u- u^{p}) in a smooth bounded domain (Omega subset {mathbb {R}}^{N},) (Nge 2,) equipped with the sublinear Neumann boundary condition (frac{partial u}{partial nu } = mu u^{q}) on (partial Omega ,) where (0<q<1<p,) and (mu ge 0) is a parameter. With sub- and supersolutions and a comparison principle for the equation, we analyze the asymptotic profile of the unique positive solution for the equation as (mu rightarrow infty .)

We consider the (L^{2})-boundedness of the solution of the Cauchy problem for a wave equation with time-dependent wave speeds. We treat it in the one-dimensional Euclidean space (textbf{R}). We adopt a simple multiplier method by using a special property of the one dimensional space.