Research Article Dead Core Problems for Singular Equations with -Laplacian
نویسندگان
چکیده
Throughout the paper L1[a,b] denotes the set of integrable functions on [a,b], Lloc(a,b] the set of functions x : (a,b]→ R which are integrable on [a− ε,b] for arbitrary small ε > 0, AC[a,b] is the set of absolutely continuous function on [a,b], and ACloc(a,b] is the set of functions x : (a,b]→ R which are absolutely continuous on [a− ε,b] for arbitrary small ε > 0. Let T be a positive number. If G⊂R j ( j = 1,2) then Car([0,T]×G) stands for the set of functions h : [0,T]×G→R satisfying the local Carathéodory conditions on [0,T]×G, that is, (j) for each z ∈ G, the function h(·,z) : [0,T]→ R is measurable; (jj) for a.e. t ∈ [0,T], the function h(t,·) : G→R is continuous; (jjj) for each compact set M ⊂ G, there exists δM ∈ L1[0,T] such that |h(t,z)| ≤ δM(t) for a.e. t ∈ [0,T] and all z ∈M. We will write h∈ Car((0,T]×G) if h∈ Car([a,T]×G) for each a∈ (0,T]. We consider the singular boundary value problem
منابع مشابه
Positive and Dead-Core Solutions of Two-Point Singular Boundary Value Problems with -Laplacian
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