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<p>In this article we study the existence of solutions for a family of perturbed eigenvalue problems described by a system consisting of two partial differential equations in which the differential operators involved are the sum between a <i>p</i>-Laplacian and a <i>q</i>-Laplacian with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(q\ne p\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>≠</mo> <mi>p</mi> </mrow> </math></EquationSource> </InlineEquation> but depending on <i>p</i>. Next, we study the asymptotic behavior, as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p\rightarrow \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">→</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, of the sequence of solutions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions.</p>

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The asymptotic behavior of solutions for a perturbed system of eigenvalue problems

  • 期刊论文

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  • 发表日期：

    2026年3月12日

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  • Anisia Teca

摘要

In this article we study the existence of solutions for a family of perturbed eigenvalue problems described by a system consisting of two partial differential equations in which the differential operators involved are the sum between a p-Laplacian and a q-Laplacian with \(q\ne p\) q ≠ p but depending on p. Next, we study the asymptotic behavior, as \(p\rightarrow \infty \) p → ∞ , of the sequence of solutions and we show that, passing eventually to a subsequence, it converges uniformly to a certain limit given by a pair of continuous functions. Moreover, we identify the limiting equations which have as solutions the limiting functions.