Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Mathematics
Dead Cores Of Singular Dirichlet Boundary Value Problems With Φ-Laplacian, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk
Dead Cores Of Singular Dirichlet Boundary Value Problems With Φ-Laplacian, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk
Mathematics and System Engineering Faculty Publications
The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem (ϕ(u′))′ = λf(t, u, u′), u(0) = u(T) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable.
Existence To Singular Boundary Value Problems With Sign Changing Nonlinearities Using An Approximation Method Approach, Haishen Lu, Donal O'Regan, Ravi P. Agarwal
Existence To Singular Boundary Value Problems With Sign Changing Nonlinearities Using An Approximation Method Approach, Haishen Lu, Donal O'Regan, Ravi P. Agarwal
Mathematics and System Engineering Faculty Publications
This paper studies the existence of solutions to the singular boundary value problem {−u′′=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), {−u″=g(t,u)+(h,u),t∈(0,1),u(0)=0=u(1), , where g: (0, 1) × (0, ∞) → ℝ and h: (0, 1) × [0, ∞) → [0, ∞) are continuous. So our nonlinearity may be singular at t = 0, 1 and u = 0 and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.