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Differential equation with several variables in the function

I have a differential equation were the function F[.] depends on
several varibles,x,y,z. I would like to solve the differential
equation for the entire function. However, I only manage to get
solutions from Mathematica if I have one variable in the function. For
example DSolve[egn==0, F[x],x]. If i try to solve for my entire
function F[x+y+z] using DSolve[egn==0, F[x+y+z],x] or even just add 1
to the function (F[x+1]) I get the error message "DSolve::litarg: To
avoid possible ambiguity, the arguments of the dependent variable in
XXX should literally match the independent variables."

Does anybody have some good suggestions?

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