Search results for "multiple solutions"

Periodic solutions for a class of second-order Hamiltonian systems

2005

Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence result of two distinct periodic solutions is given.© 2005 Texas State University - San Marcos.

Existence and multiplicity of solutions for non linear elliptic Dirichlet systems

2012

The existence and multiplicity of solutions for systems of nonlinear elliptic equations with Dirichlet boundary conditions is investigated. Under suitable assumptions on the potential of the nonlinearity, the existence of one, or two, or three solutions is established. Our approach is based on variational methods.

Multiple solutions for a mixed boundary value problem

2010

Non-homogeneous Dirichlet problems with concave-convex reaction

2022

The variational methods are adopted for establishing the existence of at least two nontrivial solutions for a Dirichlet problem driven by a non-homogeneous differential operator of p-Laplacian type. A large class of nonlinear terms is considered, covering the concave-convex case. In particular, two positive solutions to the problem are obtained under a (p -1)-superlinear growth at infinity, provided that a behaviour less than (p -1)-linear of the nonlinear term in a suitable set is requested.