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Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems

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Abstract

The paper presents the conditions which guarantee that for some positive value of ì there are positive solutions of the di.erential equation (φ(x'))'+μQ(t, x, x') = 0 satisfying the Dirichlet boundary conditions x(0) = x(T) = 0. Here Q is a continuous function on the set [0, T] × (0,∞) × (ℝ \ {0}) of the semipositone type and Q is singular at the value zero of its phase variables.

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References

  1. Agarwal, R. P., O’Regan, D., Stan¡ek, S.: Positive solutions of non-positone Dirichlet boundary value problems with singularities in the phase variables. to appear

  2. Agarwal, R. P., O’Regan, D.: Semipositone Dirichlet boundary value problems with singular dependent nonlinearities. Houston J. Math., 30, 297–308 (2004)

    MATH  Google Scholar 

  3. Jiang, D., Xu, X., O’Regan, D., Agarwal, R. P.: Multiple positive solutions to semipositone Dirichlet boundary value problems with singular dependent nonlinearities. Fasc. Math., 34, 25–37 (2004)

    MATH  Google Scholar 

  4. Afrouzi, G. A., Moghaddam, M. K.: Nonnegative solution curves of semipositone problems with Dirichlet boundary conditions. Nonlin. Anal., 61, 485–489 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gadam, S., Iaia, J. A.: Exact multiplicity of positive solutions in semipositone problems with concave-convex type nonlinearities. Electron. J. Qual. Theory Differ. Equ., 9, (2001)

  6. Cheng, J.: Exact number of positive solutions for a class of semipositone problems. J. Math. Anal. Appl., 280, 197–208 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Liu, Y.: Twin solutions to singular semipositone problems. J. Math. Anal. Appl., 286, 248–260 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Rachůnková, I., Staněk, S.: Sign-changing solutions of singular Dirichlet boundary value problems. Archives of Inequalities and Applications, 1, 11–30 (2003)

    MathSciNet  Google Scholar 

  9. Sánchez, J., Ubilla, P.: Uniqueness results for the one-dimensional m-Laplacian considering superlinear nonlinearities. Nonlinear Anal., 54, 927–938 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ma, Y., Ma, R.: Existence of positive solutions for superlinear semipositone boundary value problems that nonlinearity satisfies Carathéodory’s conditions. Acta Anal. Funct. Appl., 3, 250–255 (2001)

    MATH  MathSciNet  Google Scholar 

  11. Ma, R., Wang, R., Ren, L.: Existence results for semipositone boundary value problems. Acta Math. Sci., Ser. B, Engl. Ed., 21, 189–195 (2001)

    MATH  MathSciNet  Google Scholar 

  12. Ma, R.: Existence of positive solutions for superlinear semipositone m-point boundary value problems. Proc. Edinburgh Math. Soc., II. Ser., 46, 279–292 (2003)

    Article  MATH  Google Scholar 

  13. Ma, R.Y., Ma, Q.Z.: Positive solutions for semipositone m-point boundary-value problems. Acta Mathematica Sinica, English Series, 20(2), 273–282 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Bartle, R. G.: A Modern Theory of Integration, American Mathematical Society, Providence, RI, 2001

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Authors and Affiliations

  1. Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 77900, Olomouc, Czech Republic

    Svatoslav Staněk

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  1. Svatoslav Staněk
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Correspondence to Svatoslav Staněk.

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This work is supported by Grant No. 201/04/1077 of the Grant Agency of Czech Republic and by the Council of Czech Government MSM 6198959214

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Staněk, S. Existence of Positive Solutions to Semipositone Singular Dirichlet Boundary Value Problems. Acta Math Sinica 22, 1891–1914 (2006). https://doi.org/10.1007/s10114-005-0843-7

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  • DOI: https://doi.org/10.1007/s10114-005-0843-7

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