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Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity

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Abstract

In this paper, we establish the existence of a ground state solution for a weighted fourth-order equation of Shrödinger type under boundary Dirichlet condition in the unit ball B of ℝ4. The potential V is a continuous positive function bounded away from zero in B. The nonlinearity of the equation is assumed to have exponential growth due to Adams-type inequalities combined with polynomial term. We use the constrained minimization in the Nehari set, the quantitative deformation lemma, and degree theory results.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Exact Sciences, Frères Mentouri Constantine 1 University, Constantine, Algeria

    Rima Chetouane

  2. Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, 21955, P.O. Box 14035, Holly Makkah, Saudi Arabia

    Brahim Dridi

  3. Department of Mathematics, Faculty of Science of Tunis, University of Tunis El Manar, Tunis, Tunisia

    Rached Jaidane

Authors
  1. Rima Chetouane
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  2. Brahim Dridi
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  3. Rached Jaidane
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Correspondence to Brahim Dridi.

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Chetouane, R., Dridi, B. & Jaidane, R. Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity. Lith Math J 63, 444–465 (2023). https://doi.org/10.1007/s10986-023-09617-9

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  • DOI: https://doi.org/10.1007/s10986-023-09617-9

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