Multiple solutions for a BVP on $${(0,+\infty)}$$ ( 0 , + ∞ ) via Morse theory and $${H^1_{0,p}(\mathbb{R}^+)}$$ H 0 , p 1 ( R + ) versus $${C^1_{p}(\mathbb{R}^+)}$$ C p 1 ( R + ) local minimizers
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