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【期刊论文】Existence and multiplicity of solutions for p(x)-Laplacian equations in RN
范先令
,-0001,():
-1年11月30日
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【期刊论文】Existence of solutions for p(x)-Laplacian Dirichlet problem☆
范先令, Xian-Ling Fan*, Qi-HuZhang
Nonlinear Analysis 52(2003)1843-1852,-0001,():
-1年11月30日
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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【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
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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