We consider stationary anisotropic higher-order partial integrodifferential equations with variable exponents of nonlinearity. It is assumed that the unknown function may nonlinearly enter into the integrand. We establish the conditions of existence and uniqueness of generalized solutions of the Dirichlet problem for these equations.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 1, pp. 19–30, January–March, 2013.
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Bokalo, M.M., Domanska, O.V. Dirichlet Problem for Stationary Anisotropic Higher-Order Partial Integrodifferential Equations with Variable Exponents of Nonlinearity. J Math Sci 201, 17–31 (2014). https://doi.org/10.1007/s10958-014-1970-4
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DOI: https://doi.org/10.1007/s10958-014-1970-4