On $$L_w^2 $$ -quasi-derivatives for solutions of perturbed general quasi-differential equations

ON QUASI-INTEGRO DIFFERENTIAL EQUATIONS AND THEIR SOLUTIONS IN Lp-SPACES

“…In analogy to the adjoint and the transpose of a matrix, there are two different "(formal) adjoint" of a quasi-differential expression, we refer to [2][3][4][5] and [7][8][9][10] for more details.…”

“…In the singular problem, we first introduce the operators to be their respective closures (see [2][3][4][5], [7][8][9][10], and [19]). We denote the domains of ( )…”

“…by [3], [7][8][9], and [12][13][14][15][16], a solution of the equation is constant which is independent of λ , t…”

“…). Yang and Zettl [14][15][16][17] In [7][8][9], Ibrahim extends their results for a general quasi-differential expression τ of arbitrary order n with complex coefficients, and considered the property of boundedness of solutions of a general quasiintegro differential equations.…”

“…Our objective in this paper is to extend the results in [6][7][8][9] and [14][15][16][17][18] to a general quasi-integro differential equations with their solutions in the space ( ).…”