Multiplicity of solutions to a potential operator equation and its applications. (English) Zbl 1474.35686

Summary: We consider the multiplicity of solutions for operator equation involving homogeneous potential operators. With the help of Nehari manifold and fibering maps, we prove that such equation has at least two nontrivial solutions. Furthermore, we apply this result to prove the existence of two nonnegative solutions for three types of quasilinear elliptic systems involving \((p, q)\)-Laplacian operator and concave-convex nonlinearities.


35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35A15 Variational methods applied to PDEs
35J57 Boundary value problems for second-order elliptic systems
35J62 Quasilinear elliptic equations
Full Text: DOI


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