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Multiple solutions for non-homogeneous degenerate Schrödinger equations in cone Sobolev spaces

Author

Listed:
  • Mohsen Alimohammady

    (Faculty of Mathematical Sciences University of Mazandaran)

  • Ali Asghar Jafari

    (Faculty of Mathematical Sciences University of Mazandaran)

  • Morteza Koozehgar Kalleji

    (Arak University)

Abstract

The present paper deals with the study of semilinear and non-homogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p ∈ (2, 2∗) with respect to non-homogeneous term g(x) ∈ L 2 n/2 (B), which helps to find multiple solutions of our problem. More precisely, we prove the existence of two solutions to the problem 1.1 with negative and positive energy in cone Sobolev space H 2,0 1,n/2 (B). Finally, we consider p = 2 and we prove the existence and uniqueness of Fuchsian-Poisson problem.

Suggested Citation

  • Mohsen Alimohammady & Ali Asghar Jafari & Morteza Koozehgar Kalleji, 2017. "Multiple solutions for non-homogeneous degenerate Schrödinger equations in cone Sobolev spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 48(1), pages 133-146, March.
    • Handle: RePEc:spr:indpam:v:48:y:2017:i:1:d:10.1007_s13226-017-0215-x
    DOI: 10.1007/s13226-017-0215-x
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