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Existence of one-signed solutions of nonlinear four-point boundary value problems

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Abstract

In this paper, we are concerned with the existence of one-signed solutions of four-point boundary value problems

$$ - u'' + Mu = rg(t)f(u),u(0) = u(\varepsilon ),u(1) = u(1 - \varepsilon ) $$

and

$$u'' + Mu = rg(t)f(u),u(0) = u(\varepsilon ),u(1) = u(1 - \varepsilon ) $$

, where ε ∈ (0, 1/2), M ∈ (0,∞) is a constant and r > 0 is a parameter, g ∈ C([0, 1], (0,+∞)), f ∈ C(ℝ,ℝ) with sf(s) > 0 for s ≠ 0. The proof of the main results is based upon bifurcation techniques.

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, P.R. China

    Ruyun Ma & Ruipeng Chen

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  1. Ruyun Ma
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  2. Ruipeng Chen
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Correspondence to Ruyun Ma.

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Supported by the NSFC (No. 11061030), the Fundamental Research Funds for the Gansu Universities.

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Ma, R., Chen, R. Existence of one-signed solutions of nonlinear four-point boundary value problems. Czech Math J 62, 593–612 (2012). https://doi.org/10.1007/s10587-012-0052-3

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  • DOI: https://doi.org/10.1007/s10587-012-0052-3

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