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

In: Differential and Integral Inequalities

Author

Listed:
  • Dumitru Motreanu

    (Université de Perpignan)

  • Viorica Venera Motreanu

    (Collège Jean Moulin)

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.

Suggested Citation

  • Dumitru Motreanu & Viorica Venera Motreanu, 2019. "(p, q)–Laplacian Equations with Convection Term and an Intrinsic Operator," Springer Optimization and Its Applications, in: Dorin Andrica & Themistocles M. Rassias (ed.), Differential and Integral Inequalities, pages 589-601, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-27407-8_22
    DOI: 10.1007/978-3-030-27407-8_22
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