MULTIPLE SOLUTIONS FOR NON-HOMOGENEOUS DEGENERATE SCHRODINGER EQUATIONS IN CONE SOBOLEV SPACES

作者：Alimohammady Mohsen^*; Jafari Ali Asghar; Kalleji Morteza Koozehgar

来源：Indian Journal of Pure and Applied Mathematics, 2017, 48(1): 133-146.

DOI：10.1007/s13226-017-0215-x

• Semilinear elliptic equation
• non-homogeneous Schrodinger equation
• degenerate elliptic equations
• con Sobolev space

The present paper deals with the study of semilinear and non-homogeneous Schrodinger equations on a manifold with conical singularity. We provide a suitable constant by Sobolev embedding constant and for p is an element of (2, 2*) with respect to non-homogeneous term g(x) is an element of 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.

• 出版日期2017-3