| Summary: | In this work, we provide conditions for the existence of periodic solutions to nonlinear, second-order difference equations of the form <inline-formula><math display="inline"><semantics><mrow><mi>y</mi><mo>(</mo><mi>t</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>+</mo><mi>b</mi><mi>y</mi><mo>(</mo><mi>t</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>+</mo><mi>c</mi><mi>y</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>g</mi><mo>(</mo><mi>y</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></mrow></semantics></math></inline-formula>, where <i>b</i> and <i>c</i> are real parameters, <inline-formula><math display="inline"><semantics><mrow><mi>c</mi><mo>≠</mo><mn>0</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mrow><mi>g</mi><mo>:</mo><mi mathvariant="double-struck">R</mi><mo>→</mo><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula> is continuous.
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