Scholarlink

<p>In this paper we prove existence and regularity of solutions to a Hamiltonian system of second order elliptic equations in a bounded domain in two dimensions, where one of the nonlinearities has exponential growth and the other shows arbitrary behavior at infinity. We use the method of reduction by inversion, transforming the system into a fourth-order nonlinear elliptic equation that induces a notion of weak solution in a nonreflexive Orlicz–Sobolev space. These results improve and complement some recent works studying the critical situation of these systems.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Hamiltonian systems in two dimensions by variational methods in nonreflexive spaces

  • 期刊论文

  • 发表日期：

    2025年2月7日

查看全文
  • Maria do Desterro,
  • Elisandra Gloss,
  • Bruno Ribeiro

摘要

In this paper we prove existence and regularity of solutions to a Hamiltonian system of second order elliptic equations in a bounded domain in two dimensions, where one of the nonlinearities has exponential growth and the other shows arbitrary behavior at infinity. We use the method of reduction by inversion, transforming the system into a fourth-order nonlinear elliptic equation that induces a notion of weak solution in a nonreflexive Orlicz–Sobolev space. These results improve and complement some recent works studying the critical situation of these systems.