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On the nonlinear Neumann problem with critical and supercritical nonlinearities

100%

Chabrowski J., Tonkes E.

Instytut Matematyczny Polskiej Akademii Nauk

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coefficients Q and h are at least continuous. Moreover Q is positive on Ω̅ and λ > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coefficients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by -Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

On elliptic systems pertaining to the Schrödinger equation

94%

Chabrowski J., Tonkes E.

Annales Polonici Mathematici

2003

tom 81

nr 3

273-294

We discuss the existence of solutions for a system of elliptic equations involving a coupling nonlinearity containing a critical and subcritical Sobolev exponent. We establish the existence of ground state solutions. The concentration of solutions is also established as a parameter λ becomes large.

Ograniczanie wyników

1 Annales Polonici Mathematici

2 Chabrowski J.

2 Tonkes E.

2 2003

Wyniki wyszukiwania

On the nonlinear Neumann problem with critical and supercritical nonlinearities

On elliptic systems pertaining to the Schrödinger equation