Some Boundary Value Problems For P(x)-Laplacian Differential Equations

In this paper, we use the theory and methods of nonlinear functional analysis to deal with the existence of the solutions for p(x)-Laplacian equations under Dirichlet boundaryvalue and periodic boundary value conditions. We consider the cases that p(x) is aconstant, p(x)(x∈[a,b]) is a function of one variable and p(x)(x∈Ω|-(?) R~n) isradially symmetric, respectively.The main content of this paper is divided into three chapters:In chapter 2, we mainly consider: (1)and (2)where (3)f satisfies f∈C([0,T]×R~N,R~N) or f∈C(R~l×R~N,R~N) and is T- periodic with respect to t. Under the condition:(H) (?)R > 0, and a linear vector field V satisfying〈Vu,u〉>0 for all u∈R~N\{0}such that〈f(t,u),Vu〉≥0,〈f(t,u),V*u〉≥0 for all t∈[0,T] (or t∈R~l ) and u∈R~Nwith〈Vu,u〉= R,we prove that the problem (1) (resp. (2)) has at least one solution u(t) such thatIn chapter 3, we mainly discuss the weighted p(t)-Laplacian ordinary system (4)Where f∈C([a,b]×R~N,R~N), p(t)∈C([a,b],R~l) ,w(t) > 0, w(t)∈C([a,b],R~l). Under the...