189,556 research outputs found
Die Dortmunder Fehde von 1388/89 /
No full textVita."Die Arbeit ist auch in den 'Beiträgen zur Geschichte Dortmunds und der Grafschaft Mark' Heft XVIII abgedruckt": t. p. verso.Thesis (doctoral)--Universität Marburg.Bibliography: p. [67]-68.Mode of access: Internet
P2X1 and P2X5 subunits form the functional P2X receptor in mouse cortical astrocytes
No full textATP plays an important role in signal transduction between neuronal and glial circuits and within glial networks. Here we describe currents activated by ATP in astrocytes acutely isolated from cortical brain slices by non-enzymatic mechanical dissociation. Brain slices were prepared from transgenic mice that express enhanced green fluorescent protein under the control of the human glial fibrillary acidic protein promoter. Astrocytes were studied by whole-cell voltage clamp. Exogenous ATP evoked inward currents in 75 of 81 astrocytes. In the majority (~65%) of cells, ATP-induced responses comprising a fast and delayed component; in the remaining subpopulation of astrocytes, ATP triggered a smoother response with rapid peak and slowly decaying plateau phase. The fast component of the response was sensitive to low concentrations of ATP (with EC50 of ~40 nM). All ATP-induced currents were blocked by pyridoxal-phosphate-6-azophenyl-2',4'-disulfonate (PPADS); they were insensitive to ivermectin. Quantitative real-time PCR demonstrated strong expression of P2X1 and P2X5 receptor subunits and some expression of P2X2 subunit mRNAs. The main properties of the ATP-induced response in cortical astrocytes (high sensitivity to ATP, biphasic kinetics, and sensitivity to PPADS) were very similar to those reported for P2X1/5 heteromeric receptors studied previously in heterologous expression systems
Nontrivial Solutions for a Class of p-Kirchhoff Dirichlet Problem
No full textThis paper is devoted to the following p-Kirchhoff type of problems −a+b∫Ω∇updxΔpu=fx,u,x∈Ωu=0,x∈∂Ω with the Dirichlet boundary value. We show that the p-Kirchhoff type of problems has at least a nontrivial weak solution. The main tools are variational method, critical point theory, and mountain-pass theorem
p-Kirchhoff type problem with a general critical nonlinearity
No full textIn this article, we consider the p-Kirchhoff type problem
(1 + λ ∫ℝN |∇u|p + λb ∫ℝN |u|p) (-∆pu + b|u|p-2u) = ƒ(u), x ∈ ℝN,
where λ > 0, the nonlinearity ƒ can reach critical growth. Without the Ambrosetti-Robinowitz condition or the monotonicity condition on ƒ, we prove the existence of positive solutions for the p-Kirchhoff type problem. In addition, we also study the asymptotic behavior of the solutions with respect to the parameter λ → 0.Mathematic
Entire solutions for critical p-fractional Hardy Schrodinger Kirchhoff equations
No full textExistence theorems of nonnegative entire solutions of stationary critical p-fractional Hardy Schr¨odinger Kirchhoff equations are presented in this paper. The equations we treat deal with Hardy terms and critical nonlinearities and the main theorems extend several recent results on the topic. The paper contains also some open problems
Eigenvalue estimates for stationary p(x)-Kirchhoff problems
No full textUsing variational techniques we prove an eigenvalue theorem for
a stationary p(x)-Kirchhoff problem, and provide an estimate for the
range of such eigenvalues. We employ a specific family of test functions
in variable-exponent Sobolev spaces. Our approach permits to handle both
non-degenerate and degenerate Kirchhoff coefficients
Normal form and dynamics of the Kirchhoff equation
No full textWe summarize some recent results on the Cauchy problem for the Kirchhoff equation on the d-dimensional torus T^d, with initial data of size epsilon in Sobolev class. While the standard local theory gives an existence time of order epsilon^(-2), a quasilinear normal form allows to give a lower bound on the existence time of the order of epsilon^(−4) for all initial data, improved to epsilon^(−6) for initial data satisfying a suitable nonresonance condition. We also use such a normal form in an ongoing work with F. Giuliani and M. Guardia to prove existence of chaotic-like motions for the Kirchhoff equation
p-Kirchhoff type problem with a general critical nonlinearity
No full textIn this article, we consider the p-Kirchhoff type problem
where , the nonlinearity f can reach critical growth.
Without the Ambrosetti-Robinowitz condition or the monotonicity condition
on f, we prove the existence of positive solutions for the p-Kirchhoff
type problem. In addition, we also study the asymptotic behavior of the
solutions with respect to the parameter
Existence and multiplicity of solutions for p(.)-Kirchhoff-type equations
No full textThis paper is concerned with the existence and multiplicity of solutions of a Dirichlet problem for p(.)- Kirchhoff-type equatio
On the critical -Kirchhoff equation
No full textWe study a nonlocal elliptic equation of -Kirchhoff type involving the critical Sobolev exponent.
First we give sufficient conditions for the condition to hold. Then we prove some existence and multiplicity results using tools from Morse theory,
in particular, the notion of a cohomological local splitting and eigenvalues based on the Fadell-Rabinowitz cohomological index
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