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Boundary Value Problems, 2017
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In this work we study the following third order differential equation: 1 $$ Ly : = y''' + \bigl( q ( x,y ) + \lambda \bigr)y = f \in L_{2} ( \mathbb{R} ), \quad \mathbb{R}= ( - \infty,\infty ), \lambda> 0, $$ where $q(x,y) \geq1$ is a continuous function in all its variables. We will deal with the following questions: