(p, q)–Laplacian Equations with Convection Term and an Intrinsic Operator

Dumitru Motreanu () and Viorica Venera Motreanu ()
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Dumitru Motreanu: Université de Perpignan
Viorica Venera Motreanu: Collège Jean Moulin

A chapter in Differential and Integral Inequalities, 2019, pp 589-601 from Springer

Abstract: Abstract The paper introduces a new type of nonlinear elliptic Dirichlet problem driven by the (p, q)-Laplacian where the reaction term is in the convection form (meaning that it exhibits dependence on the solution and its gradient) composed with a (possibly nonlinear) general map called intrinsic operator on the Sobolev space. Under verifiable hypotheses, we establish the existence of at least one (weak) solution. A second main result deals with the uniqueness of solution. Finally, a third result provides the existence and uniqueness of solution to a problem of this type involving a translation viewed as an intrinsic operator. Examples show the applicability of these results.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-27407-8_22

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DOI: 10.1007/978-3-030-27407-8_22

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