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

Mohsen Alimohammady (), Ali Asghar Jafari () and Morteza Koozehgar Kalleji ()
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Mohsen Alimohammady: Faculty of Mathematical Sciences University of Mazandaran
Ali Asghar Jafari: Faculty of Mathematical Sciences University of Mazandaran
Morteza Koozehgar Kalleji: Arak University

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 1, 133-146

Abstract: 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.

Keywords: Semilinear elliptic equation; non-homogeneous Schrödinger equation; degenerate elliptic equations; con Sobolev space (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13226-017-0215-x

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