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<p>In this paper, we investigate the blow-up phenomenon of the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> norm of solutions to the inhomogeneous biharmonic Schrodinger equation in two distinct scenarios. First, we consider the case of negative energy, analyzing separately the cases of radial and non-radial solutions. Then, we examine the positive energy case, where the energy is below that of the ground state and the “kinetic” energy exceeds the corresponding value for the ground state, again distinguishing between radial and non-radial solutions. Our approach is based on convexity methods, employing virial identities in the analysis.</p>

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Blow-up results for inhomogeneous fourth-order nonlinear Schrödinger equation

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Renzo Scarpelli,
  • Maicon Hespanha

摘要

In this paper, we investigate the blow-up phenomenon of the \(H^2\) H 2 norm of solutions to the inhomogeneous biharmonic Schrodinger equation in two distinct scenarios. First, we consider the case of negative energy, analyzing separately the cases of radial and non-radial solutions. Then, we examine the positive energy case, where the energy is below that of the ground state and the “kinetic” energy exceeds the corresponding value for the ground state, again distinguishing between radial and non-radial solutions. Our approach is based on convexity methods, employing virial identities in the analysis.