Existence of solutions of abstract non-autonomous second order integro-differential equations
نویسندگان
چکیده
منابع مشابه
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and Applied Analysis 3 Let us consider the functional I x defined on H1 0 0, 2γτ by I x ∫2γτ 0 [ x′ t x′ t − τ − F t, x t , x t − τ dt. 2.4 For all x, y ∈ H1 0 0, 2γτ and ε > 0, we know that I ( x εy ) I x ε (∫2γτ 0 [ x′ t y′ t − τ x′ t − τ y′ t −Ft, x t εy t , x t − τ εy t − τ ) − F t, x t , x t − τ dt ) ε2 ∫2γτ 0 y′ t y′ t − τ dt. 2.5 It is then easy to see that 〈 I ′ x , y 〉 ∫2γτ 0 [ x′ t y′...
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ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2016
ISSN: 1687-2770
DOI: 10.1186/s13661-016-0675-7