Existence of solutions to nonlinear, subcritical higher order elliptic Dirichlet problems |
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Authors: | Wolfgang Reichel |
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Institution: | a Institut für Analysis, Universität Karlsruhe, D-76128 Karlsruhe, Germany b Institut für Mathematik, Goethe-Universität Frankfurt, D-60054 Frankfurt, Germany |
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Abstract: | We consider the 2m-th order elliptic boundary value problem Lu=f(x,u) on a bounded smooth domain Ω⊂RN with Dirichlet boundary conditions on ∂Ω. The operator L is a uniformly elliptic linear operator of order 2m whose principle part is of the form . We assume that f is superlinear at the origin and satisfies , , where are positive functions and q>1 is subcritical. By combining degree theory with new and recently established a priori estimates, we prove the existence of a nontrivial solution. |
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Keywords: | primary 35J40 secondary 35B45 |
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