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Nontrivial Solutions for the <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mn>2</mn> <mi>n</mi> </math>th Lidstone Boundary Value Problem
In this paper, we study the existence of nontrivial solutions for the <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mn>2</mn> <mi>n</mi> </math> th Lidstone boundary value problem with a sign-changing nonlinearity. Under some conditions involving the eigenvalues of a linear operator, we use the topological degree theory to obtain our main results.