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This paper presents several su4cient conditions for the existence of solutions for the Dirichlet problem of p(x)-Laplacian -div(|▽u|p(x)-2▽u=f(x, u), x∈Ω, u=0, x∈?Ω. Especially, an existence criterion for infinite many pairs of solutions for the problem is obtained. The discussion is based on the theory of the spaces Lp(x)(Ω) and W1,p(x)(Ω).

p(， x)， -Laplacian， Integral functionals， Generalized Lebesgue-Sobolev spaces， Critical points

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2005年02月23日

【期刊论文】Hartman-type results for p(t)-Laplacian systems☆

范先令， Xian-Ling Fan*， Hong-Qing Wu， Fei-Zhi Wang

Nonlinear Analysis 52(2003)585-594，-0001，（）：

-1年11月30日

摘要

Consider the weighted p(t)-Laplacian ordinary system - (w(t)|u'(t)|p(t)-2u'(t))'+w(t)f(t,u(t))=0 in (a, b), u(a)=u(b)=0, where f ∈C([a, b]×RN, RN), w∈C([a, b], R), p∈C([a, b], R) and p(t)>1 for t∈[a, b]. It is proved that if R>0 such that 〈f(t, u), u〉≥0, t∈[a, b], u∈RN with |u|=R, then the problem has a solution u such that |u(t)|≤R for t∈[a, b]. As a corollary of this result, taking w(t)=tn-1, we obtain the existence of the radial solutions for the elliptic systems. Our result generalized the corresponding results obtained by Hartman and Mawhin.

Monotone operators， p(， t)， -Laplacian systems， Radially symmetric solutions， Hartman-type result

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兰州大学，甘肃

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