Abstract:
We consider functional-differential equations with the Dirichlet conditions and with contraction and dilatation of the arguments. Necessary and sufficient conditions are obtained under which a Garding type inequality holds. These results allow us to verify coerciveness by using a special “symbol” of the equation considered.
This publication is cited in the following 28 articles:
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A. L. Tasevich, “On a Class of Elliptic Functional–Differential Equations with Orthotropic Contractions–Expansions”, Math Notes, 114:5-6 (2023), 978
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A. Tasevich, “Analysis of functional-differential equation with orthotropic contractions”, Math. Model. Nat. Phenom., 12:6, SI (2017), 240–248
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L. Rossovskii, “Elliptic functional differential equations with incommensurable contractions”, Math. Model. Nat. Phenom., 12:6 (2017), 226
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L. E. Rossovskii, “Continuous dependence of solutions to functional differential equations on the scaling parameter”, Eurasian Math. J., 7:2 (2016), 68–74
L. E. Rossovskii, A. L. Tasevich, “The First Boundary-Value Problem for Strongly Elliptic Functional-Differential Equations with Orthotropic Contractions”, Math. Notes, 97:5 (2015), 745–758
A. L. Tasevich, “Smoothness of generalized solutions of the Dirichlet problem for strongly elliptic functional differential equations with orthotropic contractions”, Journal of Mathematical Sciences, 233:4 (2018), 541–554
L. E. Rossovskii, “Elliptic functional differential equations with contractions and extensions of independent variables of the unknown function”, Journal of Mathematical Sciences, 223:4 (2017), 351–493
L. E. Rossovskii, “The coercivity of functional differential equations”, Journal of Mathematical Sciences, 201:5 (2014), 663–672