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We study an abstract equation in a reflexive Banach space, depending on areal parameter $\lambda$. The equation is composed by homogeneous potentialoperators. By analyzing the Nehari sets, we prove a bifurcation result. In someparticular cases we describe the full bifurcation diagram, and in general, weestimate the parameter $\lambda_b$ for which the problem does not have non-zerosolution when $\lambda>\lambda_b$. We give many applications to partialdifferential equations: Kirchhoff type equations, Schr\"odinger equationscoupled with the electromagnetic field, Chern-Simons-Schr\"odinger systems anda nonlinear eigenvalue problem.

On an abstract bifurcation result concerning homogeneous potential operators with applications to PDEs