Abstract
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.
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References
R. Aris: The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts. Clarendon Press, Oxford, 1975.
R. P. Agarwal, D. O’Regan, S. Staněk: General existence principles for nonlocal boundary value problems with ϕ-Laplacian and their applications. Abstr. Appl. Anal. ID 96826 (2006), 1–30.
R. P. Agarwal, D. O’Regan, S. Staněk: Positive and dead core solutions of singular Dirichlet boundary value problems with ϕ-Laplacian. Comput. Math. Appl. 54 (2007), 255–266.
J. V. Baxley, G. S. Gersdorff: Singular reaction-diffusion boundary value problems. J. Differ. Equations 115 (1995), 441–457.
L. E. Bobisud: Behavior of solutions for a Robin problem. J. Differential Equations 85 (1990), 91–104.
L. E. Bobisud: Asymptotic dead cores for reaction-diffusion equations. J. Math. Anal. Appl. 147 (1990), 249–262.
L. E. Bobisud, D. O’Regan, W. D. Royalty: Existence and nonexistence for a singular boundary value problem. Appl. Anal. 28 (1988), 245–256.
V. Polášek, I. Rachůnková: Singular Dirichlet problem for ordinary differential equations with ϕ-Laplacian. Math. Bohem. 130 (2005), 409–425.
J. Wang, W. Gao: Existence of solutions to boundary value problems for a nonlinear second order equation with weak Carathéodory functions. Differ. Equ. Dyn. Syst. 5 (1997), 175–185.
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This work was supported by grant no. A100190703 of the Grant Agency of the Academy of Sciences of the Czech Republic and by the Council of Czech Government MSM 6198959214.
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Agarwal, R.P., O’Regan, D. & Staněk, S. Dead cores of singular Dirichlet boundary value problems with ϕ-Laplacian. Appl Math 53, 381–399 (2008). https://doi.org/10.1007/s10492-008-0031-z
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DOI: https://doi.org/10.1007/s10492-008-0031-z