Fixed points and Cauchy sequences in semimetric spacesSpringer Science and Business Media LLC - Tập 17 - Trang 541-555 - 2015
W. A. Kirk, Naseer Shahzad
There have been numerous attempts recently to extend many of the metric standard fixed point theorems to a more general semimetric context. In many instances a weakened form of the triangle inequality is involved and the space is assumed to be complete. Thus Cauchy sequences play a central role. One of the standard tests to determine when a sequence is Cauchy in a metric space (X, d) is the summat...... hiện toàn bộ
Periodic solutions for nonresonant parabolic equations on $${\mathbb {R}}^N$$ with Kato–Rellich type potentialsSpringer Science and Business Media LLC - Tập 23 Số 4 - Trang 1-32 - 2021
Ćwiszewski, Aleksander, Łukasiak, Renata
A criterion for the existence of T-periodic solutions of nonautonomous parabolic equation $$u_t = \Delta u + V(x)u + f(t,x,u)$$ , $$x\in {\mathbb {R}}^N$$ , $$t>0$$ , where V is Kato–Rellich type potential and f diminishes at infinity, will be provided. It is proved that, under the nonresonance assumption, i.e. $${\mathrm {Ker}} (\Delta + V)=\{0\}$$ , the equation admits a T-periodic solution. ...... hiện toàn bộ
Iteration formulae for brake orbit and index inequalities for real pseudoholomorphic curvesSpringer Science and Business Media LLC - Tập 24 - Trang 1-30 - 2022
Beijia Zhou
I give precise iteration formulae for brake orbits in dimension 3 and use these formulae to get some index inequalities for moduli spaces of real pseudoholomorphic curves, which are important to establish real embedded contact homology and real cylindrical contact homology in dimension 3.
Multiple solutions of problems with nonlinear first-order differential operatorsSpringer Science and Business Media LLC - Tập 17 - Trang 23-42 - 2015
N. El Khattabi, M. Frigon, N. Ayyadi
In this paper, we establish the existence of solutions to firstorder differential equations with nonlinear differential operators satisfying the periodic boundary value or the initial value conditions. Notions of upper and lower solutions are introduced. Multiplicity results are also presented.
On scalar field equations with critical nonlinearitySpringer Science and Business Media LLC - Tập 4 - Trang 97-106 - 2008
Kyril Tintarev
The paper concerns existence of solutions to the scalar field equation
(0.1)
$$-\triangle u = f(u),\quad u > 0\,\,\rm{in}\,\,\mathbb{R}^{N},\quad u\,\in\,\mathcal{D}^{1,2}(\mathbb{R}^{N}), N > 2,$$
when the nonlinearity f(s) is of the critical magnitude
...... hiện toàn bộ
Strongly relatively nonexpansive sequences in Banach spaces and applicationsSpringer Science and Business Media LLC - Tập 5 - Trang 201-225 - 2009
Koji Aoyama, Fumiaki Kohsaka, Wataru Takahashi
We introduce the concept of a strongly relatively nonexpansive sequence in a Banach space and investigate its properties. Then we apply our results to the problem of approximating a common fixed point of a countable family of relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space.
Multiple ordered solutions for a class of quasilinear problem with oscillating nonlinearitySpringer Science and Business Media LLC - Tập 26 - Trang 1-19 - 2024
Gelson C. G. dos Santos, Julio Roberto S. Silva
In this paper, we use truncation argument combined with method of minimization, argument of comparison, topological degree arguments and sub-supersolutions method to show existence of multiple positive solutions (which are ordered in the
$$C(\overline{\Omega })$$
-norm) for the following class of p...... hiện toàn bộ
Stability of the braid types defined by the symplecticmorphisms preserving a linkSpringer Science and Business Media LLC - Tập 26 - Trang 1-15 - 2024
Guanheng Chen
Fix a suitable link on the disk. Recently, F. Morabito associates each Hamiltonian symplecticmorphism preserving the link to a braid type. Based on this construction, Morabito defines a family of pseudometrics on the braid groups by using the Hofer metric. In this paper, we show that two Hamiltonian symplecticmorphisms define the same braid type provided that their Hofer distance is sufficiently s...... hiện toàn bộ