臺灣博碩士論文加值系統

This paper is devoted to a class of elliptic problems

with 0 < u(x) < 1 in a bounded domain
 RN(N  1): Hence  and p are positive
parameters and f(x) 2 C(
) is a nonnegative function. By the sub-super solutions
method we show that there exists a critical parameter  = (; p; f) such that (S)
has at least one solution including a unique minimal solution for  2 (0; ) and no
solution for  > : Moreover we get the rigorous bounds on : We also discuss
properties of minimal solutions of (S) including regularity and monotonicity.

1 Introduction.

2 The pull-in voltage.
2-1 Existence of the pull-in voltage.
2-2 Monotonicity results for pull-in voltage.

3 Estimates for the pull-in voltage.
3.1 Lower bounds for λ*
3.2 Upper bounds for λ*

4 The branch of minimal solutions.
4-1 Spectral properties of minimal solutions.

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