Scholarlink

<p>This paper investigates the existence of solutions to a quasilinear Dirichlet system involving anisotropic differential operators with competing nonlinearities. We study weak, generalized, and strong generalized solutions on a bounded domain in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </math></EquationSource> </InlineEquation> using Galerkin’s approximation method. The system features nonhomogeneous growth conditions and lacks standard ellipticity and monotonicity properties due to the presence of competing (<i>p</i>,&#xa0;<i>q</i>)-Laplacian terms. Under appropriate hypotheses, we establish the existence of solutions and discuss their qualitative properties. Our results extend previous work on isotropic problems to the anisotropic setting, providing new insights into systems with convection terms.</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

Non-variational Solutions for Anisotropic (p, q)-Laplacian Systems with Nonhomogeneous Growth

  • 期刊论文

  • 发表日期：

    2025年11月22日

查看全文
  • Abdolrahman Razani,
  • Sami Baraket

摘要

This paper investigates the existence of solutions to a quasilinear Dirichlet system involving anisotropic differential operators with competing nonlinearities. We study weak, generalized, and strong generalized solutions on a bounded domain in \(\mathbb {R}^N\) R N using Galerkin’s approximation method. The system features nonhomogeneous growth conditions and lacks standard ellipticity and monotonicity properties due to the presence of competing (p, q)-Laplacian terms. Under appropriate hypotheses, we establish the existence of solutions and discuss their qualitative properties. Our results extend previous work on isotropic problems to the anisotropic setting, providing new insights into systems with convection terms.