scholarly journals A Boundary Value Problem for Noninsulated Magnetic Regime in a Vacuum Diode

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 617
Author(s):  
Edixon M. Rojas ◽  
Nikolai A. Sidorov ◽  
Aleksandr V. Sinitsyn
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Boundary Value ◽  
Singular System ◽  
Degree Theory ◽  
Fredholm Integral Equations ◽  
Topological Degree Theory ◽  
System Of Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Nonlinear Singular System

In this paper, we study the stationary boundary value problem derived from the magnetic (non) insulated regime on a plane diode. Our main goal is to prove the existence of non-negative solutions for that nonlinear singular system of second-order ordinary differential equations. To attain such a goal, we reduce the boundary value problem to a singular system of coupled nonlinear Fredholm integral equations, then we analyze its solvability through the existence of fixed points for the related operators. This system of integral equations is studied by means of Leray-Schauder’s topological degree theory.

scholarly journals A mixed boundary value problem of a cracked elastic medium under torsion

2021 ◽  
pp. 10-10
Author(s):  
Belkacem Kebli ◽  
Fateh Madani
Keyword(s):  
Boundary Value Problem ◽  
Elastic Medium ◽  
Integral Equations ◽  
Integral Transformation ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Crack Problem ◽  
Fredholm Integral Equations ◽  
Mixed Boundary Value Problem ◽  
Penny Shaped Crack

The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some particular cases of the problem.

scholarly journals Bifurcation from Interval and Positive Solutions of a Nonlinear Second-Order Dynamic Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hua Luo
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scale ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Global Bifurcation ◽  
Degree Theory ◽  
Second Order ◽  
Topological Degree Theory ◽  
Bifurcation From Interval

Let𝕋be a time scale with0,T∈𝕋. We give a global description of the branches of positive solutions to the nonlinear boundary value problem of second-order dynamic equation on a time scale𝕋,uΔΔ(t)+f(t,uσ(t))=0,  t∈[0,T]𝕋,  u(0)=u(σ2(T))=0, which is not necessarily linearizable. Our approaches are based on topological degree theory and global bifurcation techniques.

Existence Results For a Ψ-Hilfer Type Nonlocal Fractional Boundary Value Problem via Topological Degree Theory

2021 ◽  
Vol 30 (7) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K Ntouyas ◽  
Ahmed Alsaedi ◽  
Fawziah M Alotaibi
Keyword(s):  
Boundary Value Problem ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Topological Degree Theory

scholarly journals Nontrivial Solutions for the 2 n th Lidstone Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yaohong Li ◽  
Jiafa Xu ◽  
Yongli Zan
Keyword(s):  
Linear Operator ◽  
Boundary Value Problem ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Nontrivial Solutions

In this paper, we study the existence of nontrivial solutions for the 2 n th Lidstone boundary value problem with a sign-changing nonlinearity. Under some conditions involving the eigenvalues of a linear operator, we use the topological degree theory to obtain our main results.

The Problem of Several Indentors Moving on a Viscoelastic Half-Plane

1995 ◽  
Vol 62 (2) ◽  
pp. 380-389 ◽  
Author(s):  
H. Z. Fan ◽  
G. A. C. Graham ◽  
J. M. Golden
Keyword(s):  
Steady State ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Half Plane ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Mixed Boundary Value Problem ◽  
System Of Integral Equations ◽  
Space And Time

The problem of several indentors moving on a viscoelastic half-plane is considered in the noninertial approximation. The solution of this mixed boundary value problem is formulated in terms of a coupled system of integral equations in space and time. These are solved numerically in the steady-state limit for the case of two indentors. The phenomena of hysteretic friction and interaction between the two indentors are explored.

Weak solutions for a second order impulsive boundary value problem

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6431-6439
Author(s):  
Keyu Zhang ◽  
Jiafa Xu ◽  
Donal O’Regan
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Degree Theory ◽  
Point Theory ◽  
Second Order ◽  
Positive Parameter ◽  
Topological Degree Theory ◽  
Existence Of Weak Solutions ◽  
Impulsive Boundary Value Problem

In this paper we use topological degree theory and critical point theory to investigate the existence of weak solutions for the second order impulsive boundary value problem {-x??(t)- ?x(t) = f (t), t ? tj, t ? (0,?), ?x?(tj) = x?(t+j)- x?(t-j) = Ij(x(tj)), j=1,2,..., p, x(0) = x(?) = 0, where ? is a positive parameter, 0 = t0 < t1 < t2 < ... < tp < tp+1 = ?, f ? L2(0,?) is a given function and Ij ? C(R,R) for j = 1,2,..., p.

scholarly journals Antiperiodic Boundary Value Problem for a Semilinear Differential Equation of Fractional Order

2020 ◽  
Vol 34 ◽  
pp. 51-66
Author(s):  
G. G. Petrosyan ◽  
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fixed Points ◽  
Original Problem ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Existence Of A Solution ◽  
Fractional Analysis ◽  
Semilinear Differential Equation

The present paper is concerned with an antiperiodic boundary value problem for a semilinear differential equation with Caputo fractional derivative of order q ∈ (1, 2) considered in a separable Banach space. To prove the existence of a solution to our problem, we construct the Green’s function corresponding to the problem employing the theory of fractional analysis and properties of the Mittag-Leffler function . Then, we reduce the original problem to the problem on existence of fixed points of a resolving integral operator. To prove the existence of fixed points of this operator we investigate its properties based on topological degree theory for condensing mappings and use a generalized B.N. Sadovskii-type fixed point theorem.

scholarly journals Reduction of a Schwartz-type boundary value problem for biharmonic monogenic functions to Fredholm integral equations

2017 ◽  
Vol 15 (1) ◽  
pp. 374-381 ◽  
Author(s):  
Serhii V. Gryshchuk ◽  
Sergiy A. Plaksa
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fredholm Property ◽  
Fredholm Integral Equations ◽  
Cauchy Type ◽  
Simply Connected Domain ◽  
Isotropic Elasticity ◽  
Type Boundary

Abstract We consider a commutative algebra 𝔹 over the field of complex numbers with a basis {e1, e2} satisfying the conditions $ (e_{1}^{2}+e_{2}^{2})^{2}=0, e_{1}^{2}+e_{2}^{2}\neq 0. $ Let D be a bounded simply-connected domain in ℝ2. We consider (1-4)-problem for monogenic 𝔹-valued functions Φ(xe1 + ye2) = U1(x, y)e1 + U2(x, y)i e1 + U3(x, y)e2 + U4(x, y)i e2 having the classic derivative in the domain Dζ = {xe1 + ye2 : (x, y) ∈ D}: to find a monogenic in Dζ function Φ, which is continuously extended to the boundary ∂Dζ, when values of two component-functions U1, U4 are given on the boundary ∂D. Using a hypercomplex analog of the Cauchy type integral, we reduce the (1-4)-problem to a system of integral equations on the real axes. We establish sufficient conditions under which this system has the Fredholm property and the unique solution. We prove that a displacements-type boundary value problem of 2-D isotropic elasticity theory is reduced to (1-4)-problem with appropriate boundary conditions.

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