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Nonlinear Differential Equations Equivalent to Solvable Nonlinear Equations
SIAM Journal on Mathematical Analysis, 1976This paper shows in a simple and direct way the equivalence of the nonlinear differential equation $y'' + r(x)y' + q(x)Z(y) = A(y)y'^2 + g(x)z(y)[u(y)]^a $, $Z(y) = z(y)u(y)$, to the linear equation $L_1 u = g(x)$, $a = 0$, or to the nonlinear equation $L_1 u = g(x)u^a $, $a \ne 0$, where $L_1 = {{d^2 } / {dx^2 }} + r(x){d / {dx}} + q(x)$.
Klamkin, Murray S., Reid, James L.
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Nonlocal Nonlinear Schrödinger Equations
2023The authors treat here the Cauchy problem for Schrödinger equation \[ iu_ t=Au+kg[(Bu,u)]Cu,\quad u(0)=u_ 0.\leqno (1) \] Here \(u\) is a mapping of time interval \(S=[0,T)\) into a complex Hilbert space \(H\) with scalar product \((.,.),\) and \(A,B,C\) denote self-adjoint linear operators on \(H\) with densely defined domain in \(H\). Furthermore \(g\
Heimsoeth, B., Lange, H.
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2001
In this chapter we address the problem of approximationg zeros ∝ of nonlinear function f, f (∝ ) = 0, where f ϵ F ⊂ {f : D ⊂ Rd →Rl}. In order to define our solution operators, we first review several error criteria that are commonly used to measure the quality of approximations to zeros of nonlinear equations. This is done for univariate function f :
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In this chapter we address the problem of approximationg zeros ∝ of nonlinear function f, f (∝ ) = 0, where f ϵ F ⊂ {f : D ⊂ Rd →Rl}. In order to define our solution operators, we first review several error criteria that are commonly used to measure the quality of approximations to zeros of nonlinear equations. This is done for univariate function f :
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1994
Abstract The determination of roots of a given function is one of the classical mathematical problems. In most applications this problem is part of a larger one. Often it is a multi-dimensional problem. This means that we have to solve a system of nonlinear equations. Normally it is not possible to find analytical solutions. Therefore we
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Abstract The determination of roots of a given function is one of the classical mathematical problems. In most applications this problem is part of a larger one. Often it is a multi-dimensional problem. This means that we have to solve a system of nonlinear equations. Normally it is not possible to find analytical solutions. Therefore we
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Nonlinear stress-strain equations
International Journal of Solids and Structures, 1965Abstract Two unrelated methods which have previously been used in the development of stress-strain equations of nonlinear elasticity are examined. The first is the traditional notion of relating the stress to the strain through a strain energy function and the second is a recent geometrical approach suggested by Stojanovitch.
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