Displaying similar documents to “Existence theory for single and multiple solutions to singular positone discrete Dirichlet boundary value problems to the one-dimension p -Laplacian”

Existence of a positive solution to a nonlocal semipositone boundary value problem on a time scale

Christopher S. Goodrich (2013)

Commentationes Mathematicae Universitatis Carolinae

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We consider the existence of at least one positive solution to the dynamic boundary value problem - y Δ Δ ( t ) = λ f ( t , y ( t ) ) , t ∈ [ 0 , T ] 𝕋 y ( 0 ) = ∫ τ 1 τ 2 F 1 ( s , y ( s ) ) Δ s y σ 2 ( T ) = ∫ τ 3 τ 4 F 2 ( s , y ( s ) ) Δ s , where 𝕋 is an arbitrary time scale with 0 < τ 1 < τ 2 < σ 2 ( T ) and 0 < τ 3 < τ 4 < σ 2 ( T ) satisfying τ 1 , τ 2 , τ 3 , τ 4 ∈ 𝕋 , and where the boundary conditions at t = 0 and t = σ 2 ( T ) can be both nonlinear and nonlocal. This extends some recent results on second-order semipositone dynamic boundary value problems, and we illustrate these extensions with some examples.

An existence theorem of positive solutions to a singular nonlinear boundary value problem

Gabriele Bonanno (1995)

Commentationes Mathematicae Universitatis Carolinae

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In this note we consider the boundary value problem y ' ' = f ( x , y , y ' ) ( x ∈ [ 0 , X ] ; X > 0 ) , y ( 0 ) = 0 , y ( X ) = a > 0 ; where f is a real function which may be singular at y = 0 . We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. 173 (1993), 69–83], that extends and improves Theorem 3.2 of D. O’Regan [J. Differential Equations 84 (1990), 228–251].