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In this paper we study the solvability conditions under which certain partial differential equation with homogenous boundary conditions containing small parameter has a solution by using perturbation technique. Here we deal with the following partial differential equation 0 2 = + + φ φ φ w yy xx with boundary conditions 0 ) , ( ) , ( = − b x a x y y φ φ and Investigation of solvability conditions of certain boundary value problem ... ٥٥ 0 ) , ( ) , ( sin sin = − + = + = x w k b y x w k a y y x y x ε ε φ φ where w kw , are constants and ε is small parameter. According to this method, the solution of the problem is represented by the first few terms of a perturbation expansion.

Investigation of solvability conditions of certain boundary value problem by perturbation method