Results 21 to 30 of about 4,227,419 (291)
Integro-differential equations in Banach spaces and analytic resolving families of operators
Современная математика: Фундаментальные направления, 2023 We study a class of equations in Banach spaces with a Riemann–Liouville-type integro-differential operator with an operator-valued convolution kernel. The properties of \(k\)-resolving operators of such equations are studied and the class \(\mathcal A_ ...
V. E. Fedorov, A. D. Godova
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Exact solutions, Lagrangians and first integrals for generalized Camassa–Holm equation
Partial Differential Equations in Applied Mathematics, 2021 In this paper, Lagrangians and the first integrals of a new class of Liénard-type equations have been investigated. This class can be obtained using the traveling wave reduction of the generalized Camassa–Holm equation.
H. Elzehri +2 more
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To the solution of one pseudo-Volterra integral equation
Қарағанды университетінің хабаршысы. Математика сериясы, 2019 In this paper, we study a homogeneous singular integral Volterra equation of the second kind (pseudoVolterra integral equation). The singularity of the integral equation is shown. Properties of its kernel are proved.
M.T. Jenaliyev +3 more
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Gevrey class regularity for analytic differential-delay equations
Electronic Journal of Qualitative Theory of Differential Equations, 2016 This paper considers differential-delay equations of the form \[x'(t)=p(t)x(t-1),\] where the coefficient function $p\colon\mathbb{R}\rightarrow\mathbb{C}$ is analytic and not bounded on any $\delta$-neighborhood of the intervals $\left(-\infty,\gamma ...
Roger Nussbaum, Gabriella Vas
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On a class of diophantine equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 Cohn (1971) has shown that the only solution in positive integers of the equation Y(Y + 1)(Y + 2)(Y + 3) = 2X(X + 1)(X + 2)(X + 3) is X = 4, Y = 5. Using this result, Jeyaratnam (1975) has shown that the equation Y(Y + m)(Y + 2m)(Y + 3m) = 2X(X + m)(X + 2m)(X + 3m) has only four pairs of nontrivial solutions in integers given by X = 4m or −7m, Y = 5m ...
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A class of curvature type equation
Pure and Applied Mathematics Quarterly, 2021 In this paper, we study the solvability of a general class of fully nonlinear curvature equations, which can be viewed as generalizations of the equations for Christoffel-Minkowski problem in convex geometry. We will also study the Dirichlet problem of the corresponding degenerate equations as an extension of the equations studied by Krylov.
Guan, Pengfei, Zhang, Xiangwen
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Oscillation for a Class of Fractional Differential Equation
Discrete Dynamics in Nature and Society, 2013 We consider the oscillation for a class of fractional differential equation [r(t)g(D-αy)(t)]'-p(t)f∫t∞(s-t)-αy(s)ds=0, for t>0, where ...
Zhenlai Han +3 more
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A class of higher-dimensional solutions of Einstein’s vacuum equation
European Physical Journal C: Particles and Fields, 2019 A new class of higher-dimensional exact solutions of Einstein’s vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to higher-dimensional ...
Gabriel Luz Almeida, Carlos Batista
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Asymptotic Behavior of Solutions of Integral Equations with Homogeneous Kernels
Mathematics, 2022 The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined.
Oleg Avsyankin
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A class of fourth-order parabolic equation with logarithmic nonlinearity
Journal of Inequalities and Applications, 2018 In this paper, we study a class of fourth-order parabolic equation with the logarithmic nonlinearity. By using the potential well method, we obtain the existence of the unique global weak solution. In addition, we also obtain results of decay and blow-up
Pingping Li, Changchun Liu
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