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<p>In this paper it is built for the first time the sub-supersolution method in the case of a quasilinear Dirichlet problem which exhibits convection and intrinsic operator and whose principal part contains an unbounded coefficient <i>G</i>(<i>u</i>) depending on the solution <i>u</i>. A truncation technique leading to a priori estimates is developed not only for the reaction term in the equation, but also for the unbounded coefficient <i>G</i>(<i>u</i>). The existence of a solution within the sub-supersolution interval is obtained together with uniform boundedness of the solution set. A detailed example is presented.</p>

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Sub-supersolution method for problems with unbounded coefficient in the principal part

  • 期刊论文

  • 发表日期：

    2025年11月14日

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  • Roberto Livrea,
  • Dumitru Motreanu,
  • Elisabetta Tornatore

摘要

In this paper it is built for the first time the sub-supersolution method in the case of a quasilinear Dirichlet problem which exhibits convection and intrinsic operator and whose principal part contains an unbounded coefficient G(u) depending on the solution u. A truncation technique leading to a priori estimates is developed not only for the reaction term in the equation, but also for the unbounded coefficient G(u). The existence of a solution within the sub-supersolution interval is obtained together with uniform boundedness of the solution set. A detailed example is presented.