A Variational Method for the Existence of Bounded Solutions of a Sublinear Forced Oscillator
نویسندگان
چکیده
He constructed a forcing term pðtÞ in L1ðRÞ such that (1) has at least one unbounded solution. This result may look non-intuitive if the equation is interpreted as the law of motion of a non-linear oscillator. In fact, the assumptions imply that the total force gðuÞ þ pðtÞ points inwards (for large juj) and a phenomenon of resonance, as in the harmonic oscillator, seems to be excluded by the sublinear growth of g. Having this in mind, we expect that some solutions of (1) will remain bounded for an arbitrary forcing in L1ðRÞ. The main result of this paper shows that this is the case for a model non-linearity.
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