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Results tagged with difference-equations
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user 2757
Difference equations, including linear and nonlinear equations, discrete version of topics in analysis, partial difference equations, oscillation theory, periodic solutions, almost periodic solutions, bifurcation theory, stability theory.
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votes
Are there any nonlinear solutions to $f(x+1) - f(x) = f'(x)$?
Yes, there exist nonlinear solutions.
Multiplying by $e^{x+1}$ and setting $g(x):=e^x f(x)$ transforms the question into finding a solution to $g(x+1)=eg'(x)$ not of the form $e^x(ax+b)$.
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