Approximate Solution of Nonlinear Discrete Equations of Convolution Type
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By the method of potential monotone operators we prove global theorems on existence, uniqueness, and ways to find a solution for different classes of nonlinear discrete equations of convolution type with kernels of special form both in weighted and in weightless real spaces ℓ p . Using the property of potentiality of the operators under consideration, in the case of space ℓ 2 and in the case of a weighted space ℓ p (ϱ) with a generic weight ϱ, we prove that a discrete equation of convolution type with an odd power nonlinearity has a unique solution and it (the main result) can be found by gradient method.
KeywordsConvolution Monotone Operator Nonlinear Operator Weighted Space Convolution Operator
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