## On certain three-point regular boundary value problems for nonlinear second-order differential equations depending on the parameter.(English)Zbl 0845.34031

Summary: Applying a method based on a surjectivity result in $$\mathbb{R}^n$$, we investigate the existence and uniqueness of solutions of the differential equation $$x''= f(t, x, x', \lambda)$$ depending on the parameter $$\lambda$$ satisfying for a suitable value of $$\lambda$$ the three-point boundary conditions $$x'(0)= A$$, $$x(1)= B$$, $$x(2)= C$$.

### MSC:

 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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### References:

 [1] Arscott F. M.: Two-parameter eigenvalue problems in differential equations. Proc. London Math. Soc. (3), 14, 1964, 459-470. · Zbl 0121.31102 [2] Deimling K.: Nonlinear Functional Analysis. Springer-Verlag Berlin, Heidelberg, 1985. · Zbl 0559.47040 [3] Greguš M., Neuman F., Arscott F. M.: Three-point boundary value problems in differential equations. J. London Math. Soc. (2), 3, 1971, 429-436. · Zbl 0226.34010 [4] Hartman P.: Ordinary Differential Equations. J. Wiley, New York, 1964. · Zbl 0125.32102 [5] Staněk S.: Three point boundary value problem for nonlinear second-order differential equations with parameter. Czech. Math. J., 42 (117), 1992, 241-256. · Zbl 0779.34017 [6] Staněk S.: On a class of five-point boundary value problems in second-order functional differential equations with parameter. Acta Math. Hungar. 62 (3-4), 1993, 253-262. · Zbl 0801.34064 [7] Staněk S.: Multi-point boundary value problem for a class of functional differential equations with parameter. Math. Slovaca No. 1, 42 (1992), 85-96. · Zbl 0745.34066 [8] Šeda V.: A correct problem at a resonance. Differential and Integral Eqs. 2, 4 (1989), 389-396. · Zbl 0723.34020
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