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Dead cores of singular Dirichlet boundary value problems with $$\phi$$-Laplacian. (English) Zbl 1199.34076
Summary: The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem $(\phi (u'))' = \lambda f(t,u,u'),\;u(0)=u(T)=A.$ Here, $$\lambda$$ is a positive parameter, $$A>0$$, $$f$$ is singular for $$u=0$$, $$u'=0$$ and $$t=A$$.

##### MSC:
 34B16 Singular nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B09 Boundary eigenvalue problems for ordinary differential equations
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##### References:
 [1] R. Aris: The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts. Clarendon Press, Oxford, 1975. · Zbl 0315.76052 [2] R. P. Agarwal, D. O’Regan, S. Staněk: General existence principles for nonlocal boundary value problems with -Laplacian and their applications. Abstr. Appl. Anal. ID 96826 (2006), 1–30. [3] R. P. Agarwal, D. O’Regan, S. Staněk: Positive and dead core solutions of singular Dirichlet boundary value problems with -Laplacian. Comput. Math. Appl. 54 (2007), 255–266. · Zbl 1134.34010 · doi:10.1016/j.camwa.2006.12.026 [4] J. V. Baxley, G. S. Gersdorff: Singular reaction-diffusion boundary value problems. J. Differ. Equations 115 (1995), 441–457. · Zbl 0815.35019 · doi:10.1006/jdeq.1995.1022 [5] L. E. Bobisud: Behavior of solutions for a Robin problem. J. Differential Equations 85 (1990), 91–104. · Zbl 0704.34033 · doi:10.1016/0022-0396(90)90090-C [6] L. E. Bobisud: Asymptotic dead cores for reaction-diffusion equations. J. Math. Anal. Appl. 147 (1990), 249–262. · Zbl 0706.34052 · doi:10.1016/0022-247X(90)90396-W [7] L. E. Bobisud, D. O’Regan, W. D. Royalty: Existence and nonexistence for a singular boundary value problem. Appl. Anal. 28 (1988), 245–256. · Zbl 0628.34025 · doi:10.1080/00036818808839765 [8] V. Polášek, I. Rachunková: Singular Dirichlet problem for ordinary differential equations with -Laplacian. Math. Bohem. 130 (2005), 409–425. · Zbl 1114.34017 [9] 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. · Zbl 0891.34022
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