Theoretical analysis demonstrates the existence of two nontrivial solutions for p-biharmonic equations in RN, indicating structural stability under specific potential and nonlinear conditions.
This paper studies the multiplicity of solutions for a class of p-biharmonic problems posed in RN. Assuming appropriate conditions on the potential V(x) and the nonlinearities g(x,u), f(x,u), the existence of two nontrivial solutions is obtained via the Mountain Pass Theorem in conjunction with Ekeland’s variational principle.
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Zhu et al. (2026) studied this question.
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