We are concerned with the study of existence and nonexistence of weak solutions to higher order evolution inequalities with nonlinear convolution terms. We assume that the weight K(x) is a radial positive and continuous function which decreases in a neighbourhood of infinity and in the problem under consideration the nonlinearity is of the type (K*|u|^p)|u|^q, p,q>0, where * denotes the standard convolution operation. We obtain necessary conditions on and such that the above problem has solutions. Our analysis emphasizes the role played by the sign of the derivative of u respect to t of order k-1.
Higher order evolution inequalities with nonlinear convolution terms
Filippucci Roberta;
2022
Abstract
We are concerned with the study of existence and nonexistence of weak solutions to higher order evolution inequalities with nonlinear convolution terms. We assume that the weight K(x) is a radial positive and continuous function which decreases in a neighbourhood of infinity and in the problem under consideration the nonlinearity is of the type (K*|u|^p)|u|^q, p,q>0, where * denotes the standard convolution operation. We obtain necessary conditions on and such that the above problem has solutions. Our analysis emphasizes the role played by the sign of the derivative of u respect to t of order k-1.File in questo prodotto:
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