Analysis reveals multiple nontrivial solutions in semilinear 2n-order ODE, suggesting robust application of variational methods.
We consider a semilinear 2n-order problem with nonconstant coefficients. We deduce existence results by using variational methods in two directions. We primarily treat the existence when the nonlinearity has asymptotic linear behaviour at infinity and is either asymptotically sublinear or linear at zero. Secondly, we discuss the superlinear case at infinity and prove three existence results showing that our problem has at least one or two nonzero solutions.
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Chinnì et al. (2025) studied this question.
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