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The idea of the "law of the hospital" needs further exploration: is it coercive or is it, in fact, a discourse of trust?
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end{aligned} Thus, noting that (ain 0,(Gamma alpha+1))^{p}/pT^{alpha p})), we have begin{aligned}& lim_{Vert uVert _{alpha,p}rightarrowinfty}I u)=+infty, end{aligned} that is, I is coercive.
Since p − > 2 ( q + − δ ) > 2 δ , the inequality above implies that I λ ( u ) → ∞ as ∥ u ∥ X → ∞ for λ > λ ∗, that is, I λ is coercive.
(i) the functional I is coercive on W, that is I ( u ) → + ∞ as u → + ∞, u ∈ W. and bounded from below on W, (ii) the functional I is anti-coercive on V. Proof.
It remains to prove that I is coercive on X.
end{aligned} (2.9) Since (q< pleqsigma< m), from inequality (2.9), the functional I is coercive and bounded below on N. The proof is completed.
I is coercive.
So, I is coercive.
Step 1: To proof I is coercive.
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