Abstract
Abstract. We study the fifth-order degenerate differential equation of Kawahara type given in the space 𝐿2(−∞,∞). We assume that the coefficients of the equation are unbounded functions. Sufficient conditions for the correctness of the mentioned equation, as well as the maximum regularity estimate of its solution were shown in the work. According to the obtained results, if some intermediate coefficients of the equation grow rapidly to infinity then the requirement of constant sign of its smaller coefficient can be removed. Similarly, the minor coefficient can be an unbounded function. Although the coefficients of the equation are assumed to be smooth functions, no additional requirements are imposed on their first and higher order derivatives. Keywords: Kawahara equation, variable coefficient, singularity, differential operator, generalized solution, norm,
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