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2026, Volume 34, Issue 8: 5703-5722. doi: 10.3934/era.2026254
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Variational methods for fractional $ p $-Laplacian equations with mixed impulsive effects under Sturm-Liouville boundary conditions

  • School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830000, China
  • Published: 06 July 2026

  • The objective of this work is to address Sturm-Liouville boundary value problems associated with fractional $ p $-Laplacian equations, where instantaneous as well as non-instantaneous impulses are taken into account. Using variational methods, we establish the existence and multiplicity of solutions for the stated problem. The main novelty of this paper is the combination of a weakened super-$ p $-linear growth condition (which relaxes the classical Ambrosetti-Rabinowitz (AR) condition) with the concave-convex splitting technique in the mixed impulsive Sturm-Liouville $ p $-Laplacian setting. Lastly, the correctness of the key results obtained in this paper is demonstrated through an example.

    Citation: Tingting Xue. Variational methods for fractional $ p $-Laplacian equations with mixed impulsive effects under Sturm-Liouville boundary conditions[J]. Electronic Research Archive, 2026, 34(8): 5703-5722. doi: 10.3934/era.2026254

    Related Papers:

  • The objective of this work is to address Sturm-Liouville boundary value problems associated with fractional $ p $-Laplacian equations, where instantaneous as well as non-instantaneous impulses are taken into account. Using variational methods, we establish the existence and multiplicity of solutions for the stated problem. The main novelty of this paper is the combination of a weakened super-$ p $-linear growth condition (which relaxes the classical Ambrosetti-Rabinowitz (AR) condition) with the concave-convex splitting technique in the mixed impulsive Sturm-Liouville $ p $-Laplacian setting. Lastly, the correctness of the key results obtained in this paper is demonstrated through an example.



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