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.

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