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<p>We establish the existence of infinitely many weak solutions for fourth-order problems without assuming the well-known Ambrosetti–Rabinowitz hypothesis and without imposing symmetry conditions. Instead, our nonlinear term only exhibits a suitable oscillatory behavior either at infinity or at zero. In fact, we work under very general hypotheses. Our class of domains includes both smooth and non-smooth domains. Our class of nonhomogeneous differential operators includes generalized Laplace operators, generalized mean curvature operators, generalized capillarity operators, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\left( p(\cdot ), q(\cdot )\right) \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>p</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> <mo>,</mo> <mi>q</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mfenced> </math></EquationSource> </InlineEquation>-biharmonic operators, as well as new nonstandard operators.</p>

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Fourth-order problems on \(W^{2,p(\cdot )}\)-extension domains involving Leray–Lions type operators

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Maria-Magdalena Boureanu,
  • Antonia Chinnì,
  • Beatrice Di Bella

摘要

We establish the existence of infinitely many weak solutions for fourth-order problems without assuming the well-known Ambrosetti–Rabinowitz hypothesis and without imposing symmetry conditions. Instead, our nonlinear term only exhibits a suitable oscillatory behavior either at infinity or at zero. In fact, we work under very general hypotheses. Our class of domains includes both smooth and non-smooth domains. Our class of nonhomogeneous differential operators includes generalized Laplace operators, generalized mean curvature operators, generalized capillarity operators, \(\left( p(\cdot ), q(\cdot )\right) \) p ( · ) , q ( · ) -biharmonic operators, as well as new nonstandard operators.