1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1...1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.展开更多
One important MN-puzzle problem is to find a sequence of up-down and right-left movements of the empty-cell so that a goal-pattern can be achieved from a given initial-pattern.The second problem is to characterize the...One important MN-puzzle problem is to find a sequence of up-down and right-left movements of the empty-cell so that a goal-pattern can be achieved from a given initial-pattern.The second problem is to characterize the totality of the goal-pattern from a given initial-pattern.The third problem is finding the fewest movements to achieve it.In this paper,these problems will be completely solved.展开更多
文摘1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.
文摘One important MN-puzzle problem is to find a sequence of up-down and right-left movements of the empty-cell so that a goal-pattern can be achieved from a given initial-pattern.The second problem is to characterize the totality of the goal-pattern from a given initial-pattern.The third problem is finding the fewest movements to achieve it.In this paper,these problems will be completely solved.
