Geodesic
Resonance and multiplicity in periodic boundary value problems with singularity
Mathematica Bohemica, Tome 128 (2003) no. 1, pp. 45-70

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The paper deals with the boundary value problem \[ u^{\prime \prime }+k\,u=g(u)+e(t),\quad u(0)=u(2\pi ),\,\,u^{\prime }(0)=u^{\prime }(2\pi ), \] where $k\in \mathbb{R}$, $g\:I\mapsto \mathbb{R}$ is continuous, $e\in \mathbb{L}J$ and $\lim _{x\rightarrow 0+}\int _x^1g(s)\,\hspace{0.56905pt}\text{d}s=\infty .$ In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.
The paper deals with the boundary value problem \[ u^{\prime \prime }+k\,u=g(u)+e(t),\quad u(0)=u(2\pi ),\,\,u^{\prime }(0)=u^{\prime }(2\pi ), \] where $k\in \mathbb{R}$, $g\:I\mapsto \mathbb{R}$ is continuous, $e\in \mathbb{L}J$ and $\lim _{x\rightarrow 0+}\int _x^1g(s)\,\hspace{0.56905pt}\text{d}s=\infty .$ In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.
DOI : 10.21136/MB.2003.133937
Classification : 34B15, 34C25
Keywords: second order nonlinear ordinary differential equation; periodic problem; lower and upper functions 
Rachůnková, Irena; Tvrdý, Milan; Vrkoč, Ivo. Resonance and multiplicity in periodic boundary value problems with singularity. Mathematica Bohemica, Tome 128 (2003) no. 1, pp. 45-70. doi: 10.21136/MB.2003.133937
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