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On uniqueness, existence and objectivity of S-R decomposition theorem
Applied Mathematics and Mechanics, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Mian +3 more
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Linear Differential Equations: Existence and Uniqueness Theorems
1998In this section, we prove the fundamental existyence and uniqueness theorems for first-order linear ordinary differential equation. The existence proof presented here is contructive; although it does not generalized readily to nonlinear differential equations, it has its advantages over more abstract approaches to the existence theorem.(See, for ...
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An Existence and Uniqueness Theorem for Difference Equations
SIAM Journal on Mathematical Analysis, 1989The nonlinear difference equation $Py(t - k) = f(t,y(t)$ with $(j,n - j)$-conjugate boundary conditions is considered, where $Py(t - k) = 0$ is an nth-order linear difference equation and k is a fixed integer, $0 \leq k < n$. Peterson considered this type of problem for the cases $j = n - 1$ and $j = 1$. This paper extends his results to the $(j,n - j)$
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An existence and uniqueness theorem in linear elastodynamics
Meccanica, 1975Laplace transform with respect to time is applied to the boundary-initial-value problem of linear elastodynamics in order to produce a simpler elliptic boundary-value problem. Existence and uniqueness of the weak solution of the latter problem are proved.
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An existence and uniqueness theorem for the Vlasov‐Maxwell system
Communications on Pure and Applied Mathematics, 1984The purpose of the present paper is to give a local existence and uniqueness theorem for the Vlasov-Maxwell system of equations, which is one of the fundamental sets of equations underlying the kinetic theory of plasma. It is a nonlinear integro-differential system which describes the collective motion of charged particles in the presence of their own ...
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A theorem of existence and uniqueness in nonlinear optics
1979We consider quasilinear hyperbolic systems of canonical form with boundary conditions for which L. Cesari [Ann. Scuola Norm. Sup. Pisa Cl. Sci. 1 (1974), 311-358 (1975)] proved an existence and uniqueness theorem requiring among other assumptions that the two k×k matrices involved have "dominant main diagonal'' in a suitable sense and a parameter a is ...
P. BASSANINI, SALVATORI, Maria Cesarina
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A Global Existence and Uniqueness Theorem for a Riccati Equation
SIAM Journal on Mathematical Analysis, 1983It is proved that a Riccati differential equation of a particular form has a unique solution satisfying the conditions that it is to exist for large values of the independent variable t and to have its graph stay above a certain line for large t. It is then proved that the solution exists for all t.
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Nature Machine Intelligence, 2021Lu Lu, Pengzhan Jin, Guofei Pang
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