The pile driver problem via a fixed point argument

1979 ◽  
Vol 10 (2) ◽  
pp. 57-69
Author(s):  
Maurício Vieira Kritz
Keyword(s):  
Fixed Point ◽  
Pile Driver ◽  
Point Argument

THE INITIAL VALUE PROBLEM FOR THE DEEP BÉNARD CONVECTION EQUATIONS WITH DATA IN Lq

1996 ◽  
Vol 06 (02) ◽  
pp. 269-277 ◽  
Author(s):  
Z. CHARKI
Keyword(s):  
Fixed Point ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Bénard Convection ◽  
Benard Convection ◽  
Point Argument

A fixed point argument is used to prove the existence and uniqueness of solutions for the unsteady deep Bénard convection equations in [Formula: see text] for [Formula: see text].

Qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source

2016 ◽  
Vol 09 (04) ◽  
pp. 1650051
Author(s):  
Haiyan Li ◽  
Jianguo Gao
Keyword(s):  
Fixed Point ◽  
Qualitative Analysis ◽  
Global Solution ◽  
Cell Mass ◽  
Logistic Source ◽  
Unique Global Solution ◽  
Chemotaxis Model ◽  
Initial Cell ◽  
Point Argument ◽  
Moser's Iteration

In this paper, we focus on the qualitative analysis of a parabolic–elliptic attraction–repulsion chemotaxis model with logistic source. Applying a fixed point argument, [Formula: see text]-estimate technique and Moser’s iteration, we derive that the model admits a unique global solution provided the initial cell mass satisfying [Formula: see text] for [Formula: see text] While for [Formula: see text], there are no restrictions on the initial cell mass and the result still holds.

scholarly journals Constrained controllability of nonlinear stochastic impulsive systems

2011 ◽  
Vol 21 (2) ◽  
pp. 307-316 ◽  
Author(s):  
Shanmugasundaram Karthikeyan ◽  
Krishnan Balachandran
Keyword(s):  
Fixed Point ◽  
Finite Time ◽  
Stochastic Systems ◽  
Time Interval ◽  
Complete Controllability ◽  
Finite Time Interval ◽  
Impulsive Systems ◽  
Nonlinear Stochastic Systems ◽  
Constrained Controllability ◽  
Point Argument

Constrained controllability of nonlinear stochastic impulsive systemsThis paper is concerned with complete controllability of a class of nonlinear stochastic systems involving impulsive effects in a finite time interval by means of controls whose initial and final values can be assigned in advance. The result is achieved by using a fixed-point argument.

scholarly journals Positive Solutions for Resonant (p, q)-equations with convection

2020 ◽  
Vol 10 (1) ◽  
pp. 217-232 ◽  
Author(s):  
Zhenhai Liu ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Fixed Point ◽  
Dirichlet Problem ◽  
Positive Solutions ◽  
Smooth Solution ◽  
Singular Term ◽  
Phase Problem ◽  
Drift Term ◽  
Double Phase ◽  
Double Phase Problem ◽  
Point Argument

Abstract We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based on an iterative asymptotic process, we show that the problem has a positive smooth solution.

scholarly journals Well-posedness of stochastic modified Kawahara equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
P. Agarwal ◽  
Abd-Allah Hyder ◽  
M. Zakarya
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Water Wave ◽  
Well Posedness ◽  
Kawahara Equation ◽  
Fourier Restriction ◽  
The Cauchy Problem ◽  
Restriction Method ◽  
Fifth Order ◽  
Point Argument

AbstractIn this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in $H^{s}(\mathbb{R})$Hs(R), $s\geq -1/4$s≥−1/4. Moreover, we get the global existence for $L^{2}( \mathbb{R})$L2(R) solutions. Due to the non-zero singularity of the phase function, a fixed point argument and the Fourier restriction method are proposed.

scholarly journals Common Fixed Point Results of Set Valued Maps for Aφ-Contraction and Generalized ϕ-Type Weak Contraction

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 894
Author(s):  
Murchana Neog ◽  
Mohammed M. M. Jaradat ◽  
Pradip Debnath
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theory ◽  
Real Life ◽  
Point Theory ◽  
Weak Contraction ◽  
Life Problems ◽  
Ulam Theorem ◽  
The Given ◽  
Point Argument

The solutions for many real life problems may be obtained by interpreting the given problem mathematically in the form f ( x ) = x . One such example is that of the famous Borsuk–Ulam theorem in which, using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this article, some new results concerning coincidence and a common fixed point for an A φ -contraction and a generalized ϕ -type weak contraction are established. We prove our results for set valued maps without using continuity of the corresponding maps and completeness of the relevant space. Our results generalize and extend several existing results. Some new examples are given to demonstrate the generality and non-triviality of our results.

scholarly journals Existence of Positive Solution for a Nonlinear Weighted Bi-Harmonic System of Elliptic Partial Differential Equations via Fixed-Point Argument

2020 ◽  
Vol 40 (1) ◽  
pp. 54-70
Author(s):  
Md Asaduzzamana ◽  
Md Zulfikar Ali
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Positive Solution ◽  
A Priori ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Existence Criterion ◽  
Point Argument ◽  
Harmonic System

In this paper, we establish an existence criterion of positive solution for a nonlinear weighted bi-harmonic system of elliptic partial differential equations in the unit ball in Nn ( dimensionaleuclideanspace) The analysis of this paper is based on a topological method (a fixed-point argument). Initially, we establish a priori solution estimates, and then use a fixed-point theorem for deducing the existence of positive solutions. Finally, we prove a non-existence criterion as the complement of existence criterion. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 54-70

scholarly journals Random initial conditions for semi-linear PDEs

2019 ◽  
Vol 150 (3) ◽  
pp. 1533-1565
Author(s):  
Dirk Blömker ◽  
Giuseppe Cannizzaro ◽  
Marco Romito
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Stochastic Pdes ◽  
Well Posedness ◽  
Critical Spaces ◽  
Random Initial Conditions ◽  
Linear Pdes ◽  
Point Argument

AbstractWe analyse the effect of random initial conditions on the local well-posedness of semi-linear PDEs, to investigate to what extent recent ideas on singular stochastic PDEs can prove useful in this framework.In particular, in some cases, stochastic initial conditions extend the validity of the fixed-point argument to larger spaces than deterministic initial conditions would allow, but in general, it is never possible to go beyond the threshold that is predicted by critical scaling, as in our general class of equations we are not exploiting any special structure present in the equation.We also give a specific example where the level of regularity for the fixed-point argument reached by random initial conditions is not yet critical, but it is already sharp in the sense that we find infinitely many random initial conditions of slightly lower regularity, where there is no solution at all. Thus criticality cannot be reached even by random initial conditions.The existence and uniqueness in a critical space is always delicate, but we can consider the Burgers equation in logarithmically sub-critical spaces, where existence and uniqueness hold, and again random initial conditions allow to extend the validity to spaces of lower regularity which are still logarithmically sub-critical.

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