Multiple solutions for a class of nonhomogeneous semilinear equations with critical cone Sobolev exponent

Koozehgar Kalleji, Morteza; Alimohammady, Mohsen; Jafari, Ali Asghar

doi:10.1090/proc/14332

Multiple solutions for a class of nonhomogeneous semilinear equations with critical cone Sobolev exponent
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by Morteza Koozehgar Kalleji, Mohsen Alimohammady and Ali Asghar Jafari PDF

Proc. Amer. Math. Soc. 147 (2019), 597-608 Request permission

Abstract:

In this paper, we deal with the study of a class of semilinear and nonhomogeneous Schrödinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and the critical cone Sobolev exponent with respect to the nonhomogeneous term $g(x)\in L^{\frac {n}{2}}_{2}(\mathbb {B}).$ Our approach improves on and generalizes the previous results in [Indian J. Pure Appl. Math. 48 (2017), pp. 133–146] and [Ann. Global Anal. Geom. 39 (2011), pp. 27–43].

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