Results 141 to 150 of about 1,093 (183)
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Nonlinear Evolution Equations in Banach Spaces
Israel Journal of Mathematics, 1972The evolution problem 0∈du/dt+A(t)u(t),u(s)=x, where theA(t) are nonlinear operators acting in a Banach space, is studied. Evolution operators are constructed from theA(t) under various assumptions. Basic properties of these evolution operators are established and their relationship to the evolution equation is determined.
A Pazy
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Nonlinear volterra integrodifferential equations in a Banach space
Israel Journal of Mathematics, 1982We study the Cauchy problem associated with the Volterra integrodifferential equation u\left( t \right) \in Au\left( t \right) + \int {_0^1 B\left( {t - s} \right)u\left( s \right)ds + f\left( t \right),} u\left( 0 \right) = u_0 \in D\left( A \right), whereA is anm-dissipative non-linear operator (or more generally, anm-D(ω) operator), defined onD(A ...
Grimmer, Ronald, Zeman, Marvin
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On the Solution of Nonlinear Equations With Monotone Opera Tors in a Banach Space
Siberian Mathematical Journal, 1975exaly +2 more sources
on the solvability of nonlinear equations in Banach spaces
2006Using a generalization of the Borsuk Ulam theorem to multivalued maps we study the existence of solutions by means of the Lyapunov -Schmidt method even in the case when the auxiliary equation cannot be solved ...
Massabò I. +2 more
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Solvability of nonlinear equations in a cone of a banach space
Journal of Mathematical Sciences, 2000The author finds a solvability conditions for the equation \(Tu+ F(u)= 0\) in the case where the operator \([T+ F'(u)]^{-1}\) exist only for \(u\in K\), where \(K\) is a cone in a Banach space \(X\). He gives an application concerning the solvability of boundary-value problems for systems of second-order differential equations.
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Asymptotic Equivalence of Nonlinear Differential Equations in Banach Spaces
SIAM Journal on Mathematical Analysis, 1975New concepts of asymptotic equivalence of differential equations in Banach spaces are introduced. Our techniques use the comparison theorem and a result on asymptotic equilibrium in Banach spaces. As an application we extend a nonlinear perturbation result of A. G. Kartsatos.
Bernfeld, S. R. +2 more
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Nonlinear Integral Equations In Banach Spaces
1996This chapter is the main part of the book. We discuss nonlinear integral equations in Banach spaces both of the Fredholm type and the Volterra type.
Dajun Guo, V. Lakshmikantham, Xinzhi Liu
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Nonlinear equations of evolution in Banach spaces
Nonlinear Analysis: Theory, Methods & Applications, 1984The author constructs a sequence of approximate solutions which converges to a local solution of the Cauchy problem \[ dx/dt+F(t,x)=0,\quad 0\leq t\leq b,\quad x(0)=0 \] in a scale of Banach spaces with increasing norms.
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Nonlinear perturbation of linear evolution equations in a banach space
Annali di Matematica Pura ed Applicata, 1976Let X be a Banach space and {A(t)|t e [0, T]} a family of closed linear, densely defined m-accretive operators in X. This paper is concerned with the additive perturbation of {A(t)|t e [0, T]} by a continuous family of nonlinear accretive operators {B(t)|t e [0, T]}.
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