【摘 要】
：
In critical point theory,Clarks theorem states as follows.Let X be a Banach space,Φ∈C1(X,R).Assume Φ satisfies the(PS)condition,is even and bounded from
【机 构】
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CapitalNormalUniversity
【出 处】
：
非线性偏微分方程和数学物理研讨会(NPDEMP 2016)
论文部分内容阅读
In critical point theory,Clarks theorem states as follows.Let X be a Banach space,Φ∈C1(X,R).Assume Φ satisfies the(PS)condition,is even and bounded from below,and Φ(0)= 0.If for any k∈N,there exists a k-dimensional subspace Xk of X and ρk> 0 such that supXk∩Sρk Φ<0,where Sρ = {u∈X|‖u‖ = ρ},then Φ has a sequence of critical values ck<0 satisfying ck→0 as k→∞.We improve Clarks theorem by showing that under the assumptions of Clarks theorem Φ has a sequence of critical points uk such that Φ(uk)≤0 and uk→ 0 as k→∞.
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