Heteroclinic Solutions for Nonautonomous EFK Equations
نویسندگان
چکیده
and Applied Analysis 3 Lemma 3. Let q ∈ E. Then for any V > 0, r < s ∈ R such that q(t) ∉ B ε (V) and |q(t)| ⩽ V for any t ∈ [r, s], I (q) ⩾ √2σ ε,V q (r) − q (s) . (16) In particular, if σ ε > 0, then for any r < s ∈ R such that q(t) ∉ B ε (V) for any t ∈ [r, s], I (q) ⩾ √2σ ε q (r) − q (s) . (17) Proof. Denote l = |q(r) − q(s)| and τ = |r − s|. Then l = ∫ s r q (t) dt ⩽ ∫ s r q (t) dt ⩽ τ 1/2 (∫ s r q (t) 2 dt) 1/2
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