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On a singular nonlinear Neumann problem

Chabrowski J.

Opuscula Mathematica

2014

Vol. 34, no. 2

271--290

We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: (i) 2 < p+1 <2*s, (ii) p+1 = 2*(s) and (iii) 2*(s) < p+1 ≤ 2*, where [formula] denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively.

On the nonlinear Neumann problem with indefinite weight and Sobolev critical nonlinearity

Chabrowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 3

323-333

We prove the existence of positive solutions of the Neumann problem with indefinite weight and critical Sobolev nonlinearity. Our approach is based on the concentration-compactness principle applied to a related variational problem.