A DSM proof of surjectivity of monotone nonlinear mappings

A. G. Ramm

Displaying similar documents to “A DSM proof of surjectivity of monotone nonlinear mappings”

An existence result for nonlinear evolution equations of second order

Dimitrios A. Kandilakis (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we consider a second order differential equation involving the difference of two monotone operators. Using an auxiliary equation, a priori bounds and a compactness argument we show that the differential equation has a local solution. An example is also presented in detail.

On monotone solutions of linear advanced equations.

Kvinikadze, G. (1999)

Memoirs on Differential Equations and Mathematical Physics

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Lj. Kočinac (1991)

Matematički Vesnik

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$A$ -monotonicity and applications to nonlinear variational inclusion problems.

Verma, Ram U. (2004)

Journal of Applied Mathematics and Stochastic Analysis

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Monotone solutions of some differential equations

Marko Švec (1967)

Colloquium Mathematicae

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Periodic solutions for quasilinear vector differential equations with maximal monotone terms

Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We consider a quasilinear vector differential equation with maximal monotone term and periodic boundary conditions. Approximating the maximal monotone operator with its Yosida approximation, we introduce an auxiliary problem which we solve using techniques from the theory of nonlinear monotone operators and the Leray-Schauder principle. To obtain a solution of the original problem we pass to the limit as the parameter λ > 0 of the Yosida approximation tends to zero.