ON THE EXISTENCE OF EXTRENAL PERIODIC SOLUTIONS FOR NONLINEAR PARABOLIC PROBLEMS WITH DISCONTINUITIES
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概要
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In this paper we consider a very general second order nonlinear parabolic boundary value problem. Assuming the existence of an upper solution ＄￥varphi＄ and a lower solution ＄￥psi＄ satisfying ＄￥psi￥leq￥varphi＄ , we show that the problem has extrenal periodic solutions in the order interval ＄K=[￥psi)￥varphi]＄ . Our proof is based on a general surjectivity result for the sum of two operators of monotone type and on truncation and penalization techniques. In addition we use a result of independent interest which we prove here and which says that the pseudomonotonicity property of ＄A(t, ￥cdot)＄ can be lifted to its Nemitsky operator. Finally when we impose stronger conditions on the data, we show that the extrenal solutions can be obtained with a monotone iterative process.
- Yokohama City University and Yokohama National Universityの論文
- 1998-00-00
Yokohama City University and Yokohama National University | 論文
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