We study the nonlinear elliptic boundary value problem
where A is an operator of p-Laplacian type, is an unbounded domain in with non-compact boundary, and f and g are subcritical nonlinearities. We show existence of a nontrivial nonnegative weak solution when both f and g are superlinear. Also we show existence of at least two nonnegative solutions when one of the two functions f, g is sublinear and the other one superlinear. The proofs are based on variational methods applied to weighted function spaces.
Submitted March 5, 1998. Published April 10, 1998.
Math Subject Classification: 35J65, 35J20.
Key Words: p-Laplacian, nonlinear boundary condition, variational methods, unbounded domain, weighted function space.
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|Klaus Pflueger |
FB Mathematik, Freie Universitat Berlin
Arnimallee 3, 14195 Berlin, Germany
Web page: http://www.math.fu-berlin.de/user/pflueger
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