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Article Contents

# Infinitely many subharmonic solutions for nonlinear equations with singular $\phi$-Laplacian

• * Corresponding author

This work was supported by National Natural Science Foundation of China (No.11671287, No.11771105) and Guangxi Natural Science Foundation (No.2017GXNSFFA198012)

• In this paper we prove the existence and multiplicity of subharmonic solutions for nonlinear equations involving the singular $\phi$-Laplacian. Such equations are in particular motivated by the one-dimensional mean curvature problems and by the acceleration of a relativistic particle of mass one at rest moving on a straight line. Our approach is based on phase-plane analysis and an application of the Poincaré-Birkhoff twist theorem.

Mathematics Subject Classification: Primary: 34C25, 34B15; Secondary: 37C25.

 Citation:

• Figure 1.  The relations between the fundamental period $T_h$ and "energy" $h$ with various potentials: (a) Toda potential $G(x) = k(x+{\mathrm{e}}^{-x})$ with $k = 1$; (b) Sublinear potential $G(x) = \frac{4}{5}|x|^{5/4}$; (c) Harmonic potential $G(x) = \frac{1}{2}x^{2}$; (d) Superlinear potential $G(x) = \frac{2}{5}|x|^{5/2}$

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