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Generalized lower and upper functions for the φ-Laplacian

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Abstract

We give definitions of generalized lower and upper functions and generalized solution, which differs from a solution in the conventional sense in that the derivative of a generalized solution can be equal to +∞ and −∞. We show how to use generalized solutions for obtaining classical results.

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Authors and Affiliations

  1. Institute for Mathematics and Computer Science, Latvia University, Riga, Latvia

    A. Ya. Lepin & L. A. Lepin

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  1. A. Ya. Lepin
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  2. L. A. Lepin
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Correspondence to A. Ya. Lepin.

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Original Russian Text © A.Ya. Lepin, L.A. Lepin, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 5, pp. 601–610.

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Lepin, A.Y., Lepin, L.A. Generalized lower and upper functions for the φ-Laplacian. Diff Equat 50, 598–607 (2014). https://doi.org/10.1134/S0012266114050036

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  • DOI: https://doi.org/10.1134/S0012266114050036

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