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In recent years, the solvability of the antiperiodic boundary value problems of first-order and second-order differential equations were studied by many authors, for example, we refer to [20 32] and the references therein.
In some special cases, when the nonlinear term has various forms, the following nonlinear wave equation u_{tt}-Delta u=F x,t,u,u_{t}), (1.4) where Δ is a Laplace operator, has been extensively studied by many authors, for example, we refer to [1 10] and the references given therein.
The wave equation u_{tt}-Delta u=f x,t,u,u_{t}), (1.4) with different boundary conditions, has been extensively studied by many authors, for example, we refer to [1 25] and the references given therein.
For example, we refer the reader to [1, 2] and the references cited therein.
Equation (1.3) has been studied extensively by many authors, and there is a large body of literature on the existence and multiplicity of results of solutions for equation (1.3); for example, we refer the readers to [1 3] and references therein.
For example, we refer the reader to [1 6] and the references cited therein.
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"For example, we referred Celeste to the local health centre for anti-retroviral treatment, and she is doing well now," she said.
For example, we referred to patients' "poor patient-physician relationship" rather than the more encompassing "dislike of the provider" [ 13] because these patients stressed the characteristics of the relationship, rather than an overall and imprecise dislike of the provider.
For examples, we refer the reader to [16 22].
One can put conditions on the space X and the morphism ϕ so that ϕ has an α-coincidence for each (alphain operatorname{Cov}_{X} (overline{phi(X)})) would guarantee that ϕ has a coincidence; for examples we refer the reader to [7] (Lemma 1.2), [3] (Lemma 6.1), [8] (Theorem 1.4 and Remark 1.6).
For examples we refer to the two subsequent sections.
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