The authors derive structural representations for entire solutions of (p1 L(f)+p2 f(z+c)+p5 f)^2 + (p3 L(f)+p4 f(z+c)+p6 f)^2 = p in four cases based on coefficient determinants.
Hemmati, Entire solutions of first-order nonlinear partial differential equations, Vol
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On the Fermat-type partial differential-difference equations on $\mathbb{C}^n$
The authors derive structural representations for entire solutions of (p1 L(f)+p2 f(z+c)+p5 f)^2 + (p3 L(f)+p4 f(z+c)+p6 f)^2 = p in four cases based on coefficient determinants.