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On the number of radially symmetric solutions to Dirichlet problems with jumping nonlinearities of superlinear order |
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| Authors: | Alfonso Castro Hendrik J. Kuiper |
| Affiliation: | Department of Mathematics, University of North Texas, Denton, Texas 76203 Hendrik J. Kuiper ; Department of Mathematics, Arizona State University, Tempe, Arizona 85287--1804 |
| Abstract: | This paper is concerned with the multiplicity of radially symmetric solutions  to the Dirichlet problem
on the unit ball |
| Keywords: | Radially symmetric Dirichlet problem superlinear jumping nonlinearity nodal curves critical exponent. |
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with boundary condition 
on 
. Here 
is a positive function and 
is a function that is superlinear (but of subcritical growth) for large positive 
, while for large negative 
we have that 
, where 
is the smallest positive eigenvalue for 
in 
with 
on 
. It is shown that, given any integer 
, the value 
may be chosen so large that there are 
solutions with 
or less interior nodes. Existence of positive solutions is excluded for large enough values of 
.