1,720,972 research outputs found
Double resonance in sturm–liouville planar boundary value problems
Full text linkWe provide some existence results for Sturm–Liouville boundary value problems associated with the planar differential system Jz′ = g(t, z) + r(t, z) where g is suitably controlled by the gradient of two positively homogeneous functions of degree 2 and r is sublinear with respect to the variable z at infinity. We study the existence of solutions when a double resonance phenomenon occurs by the introduction of Landesman–Lazer type conditions. Applications to scalar second order differential equations are given
WELL-ORDERED AND NON-WELL-ORDERED LOWER AND UPPER SOLUTIONS FOR PERIODIC 2N-DIMENSIONAL SYSTEMS
No full textIn this paper we consider a class of periodic problems associated with 2N-dimensional systems of differential equations. Our aim is to generalize the theory of lower and upper solutions following the way paved in previous works. After a careful analysis of the dynamics in the phase space, the proofs take advantage of topological degree arguments
Non-well-ordered lower and upper solutions for semilinear systems of PDEs
Full text linkWe prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type
Non-well-ordered lower and upper solutions for semilinear systems of PDEs
Full text linkWe prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type
Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces
Full text linkWe prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well-established results for scalar equations
A Poincaré–Birkhoff theorem for multivalued successor maps with applications to periodic superlinear Hamiltonian systems
No full textWe provide a new version of the Poincaré–Birkhoff theorem for possibly multivalued successor maps associated with planar non-autonomous Hamiltonian systems. As an application, we prove the existence of periodic and subharmonic solutions of the scalar second order equation x ̈+λg(t,x)=0, for λ>0 sufficiently small, with g(t, x) having a superlinear growth at infinity, without requiring the existence of an equilibrium point
Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces
No full textWe prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well-established results for scalar equations
Multiplicity of Radial Ground States for the Scalar Curvature Equation Without Reciprocal Symmetry
Full text linkWe study existence and multiplicity of positive ground states for the scalar curvature equation Δu+K(|x|)un+2n-2=0,x∈Rn,n>2,when the function K: R+→ R+ is bounded above and below by two positive constants, i.e. 0 0 , it is decreasing in (0 , R) and increasing in (R, + ∞) for a certain R> 0. We recall that in this case ground states have to be radial, so the problem is reduced to an ODE and, then, to a dynamical system via Fowler transformation. We provide a smallness non perturbative (i.e. computable) condition on the ratio K ̄/K̲ which guarantees the existence of a large number of ground states with fast decay, i.e. such that u(| x|) ∼ | x| 2-n as | x| → + ∞, which are of bubble-tower type. We emphasize that if K(r) has a unique critical point and it is a maximum the radial ground state with fast decay, if it exists, is unique
An extension of the Poincaré–Birkhoff Theorem to systems involving Landesman–Lazer conditions
Full text linkWe provide multiplicity results for the periodic problem associated with Hamiltonian systems coupling a system having a Poincaré–Birkhoff twist-type structure with a system presenting some asymmetric nonlinearities, with possible one-sided superlinear growth. We investigate nonresonance, simple resonance and double resonance situations, by implementing some kind of Landesman–Lazer conditions
Two-point boundary value problems for planar systems: A lower and upper solutions approach
Full text linkWe extend the theory of lower and upper solutions to planar systems of ordinary differential equations with separated boundary conditions, both in the well-ordered and in the non-well-ordered cases. We are able to deal with general Sturm–Liouville boundary conditions in the well-ordered case, and we analyze the Dirichlet problem in the non-well-ordered case. Our results apply in particular to scalar second order differential equations, including those driven by the mean curvature operator. Higher dimensional systems are also treated, with the same approach
- …
