This asserts: there exists a concept G such that for every object x, x falls under G if and only if x is odd and greater than 5.
Thereby, condition allows to assert that there exists, such that for all (3.9).
First, we assert that there exists such that is completely continuous.
Also, we can assert that there exists x ∈ ( Ω ¯ 2 ∖ Ω 1 ) ∩ K such that L x = N x.
(7) We assert that there exists a positive constant (r_{1}) such that (I_{1} ( r_{1} ) >0).
Therefore, for all so large that, as is a weak solution to, by taking as the test function in(2.5), from (2.9), and, we can assert that there exists such that (2.11).
For ρ ∈ U T and with condition (A4), the assumptions of Lemma 3.3 are fulfilled, and we can assert that there exists a unique X ∈ E 1 ( R 2 ), which is a solution of (4.7).
end{aligned} (3.9) Besides, we can assert that there exists some positive constant (N_{1}) such that int^{omega}_{0}bigl|g bigl t,x_{1}bigl t-tau(t)bigr)bigr)bigr|,dtleq2omega N_{1}bigl t-taua.
We assert that there exists a positive constant M such that begin{aligned}& uleq M delta)+bar{u}_{varepsilon},quad xin Omega_{rho}^, end{aligned} (4.3) begin{aligned}& underline{u}_{varepsilon}leq u+M delta),quad xinOmega_{rho}^.
end{aligned} (3.7) Besides, we can assert that there exists some positive constant (N_{1}) such that int^{T}_{0} biglvert g bigl t,x_{1} bigl t-tau(t) bigl t-tau) bigrvert,dtleq2T N_{1}+T bigr( K+ vert evert _{infty}bigr).
