## Exact multiplicity of sign-changing solutions for a class of second-order Dirichlet boundary value problem with weight function.(English)Zbl 1470.34064

Summary: Using bifurcation techniques and Sturm comparison theorem, we establish exact multiplicity results of sign-changing or constant sign solutions for the boundary value problems $$u'' + a(t) f(u) = 0$$, $$t \in(0, 1)$$, $$u(0) = 0$$, and $$u(1) = 0$$, where $$f \in C(\mathbb{R}, \mathbb{R})$$ satisfies $$f(0) = 0$$ and the limits $$f_\infty = \lim_{| s | \rightarrow \infty}(f(s) / s)$$, $$f_0 = \lim_{| s | \rightarrow 0}(f(s) / s) \in \{0, \infty \}$$. Weight function $$a(t) \in C^1 [0, 1]$$ satisfies $$a(t) > 0$$ on $$[0, 1]$$.

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations
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### References:

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