Existence of multiple solutions for second order boundary value problems. (English) Zbl 1013.34017

The authors prove the existence of at least three solutions to nonlinear two-point boundary value problems \[ y''+ f(x,y,y')= 0,\quad x\in [0,1],\quad y(0)= 0= y(1), \] where \(f:[0,1]\times \mathbb{R}^2\to\mathbb{R}\) is continuous and satisfies the Bernstein-Nagumo condition. The proofs are based on the method of lower and upper solutions and the theory of topological degree. For earlier work, see R. Avery [Math. Sci. Res. Hot-Line 2, No. 1, 1-6 (1998; Zbl 0960.34503)].
Reviewer: Ruyun Ma (Lanzhou)


34B15 Nonlinear boundary value problems for ordinary differential equations
47H11 Degree theory for nonlinear operators


Zbl 0960.34503
Full Text: DOI


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