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In this case methods from the calculus of variations can be used and regularity of solutions can be shown.
Self-reported NSAID use in the decade prior to diagnosis was categorized by duration and regularity of use.
Influence of factors on pain level and regularity of analgesic use were investigated using linear regression.
In [2], under the above similar conditions, Qian and Li established the existence of three non-trivial solutions of (1.1) by use of mountain pass theorem and regularity of critical groups.
In multiple linear regression self efficacy and regularity of analgesic use were significant (p < 0.01) with lower self efficacy and more regular use of analgesics associated with more pain.
Increased duration and regularity of NSAID use was associated with reduced breast cancer-specific mortality in women with ER-positive tumors (long-term regular use (≥8 days/month for ≥ 3 years) versus no use; hazard ratio (HR) 0.48; 95 % confidence interval (CI) 0.23-0.98), with a statistically significant trend with increasing duration and regularity (p-trend = 0.036).
Furthermore, we examined the duration and regularity of NSAID use, which are important factors in reducing the risk of colorectal cancer by NSAIDs [ 7].
By contrast a smaller but similar study of RA patients found no relationship between pain and regularity of analgesic use [ 28].
41 The lack of a statistically significant association between aspirin use and the risk of advanced colorectal neoplasia in our study may be due to recall bias or missing data regarding the dose and regularity of aspirin use.
To overcome it, we use the regularity of L in [1].
Similarly, we can use the regularity of (w_{1}) to prove that as λ is large enough, there is β with (1 < beta< frac{2q}{q+2+2(2+alpha)}) such that int w_{1}(v_{lambda})^{2^{sharp}-1},dxi= Ccdot bigl( lambda^{-1} bigr)^{frac{q}{beta} - frac{q+2}{2}}, where we have used the assumption (0 < alpha< frac{q}{2} - 3).
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