Search results for " Multiplicity results"

Poincar é-Birkhoff fixed point theorem and periodic solutions of asymptotically linear planar Hamiltonian systems. (Turin Fortnight Lectures on Nonli…

2002

Multiplicity of solutions for asymptotically linear $n$-th order boundary value problems

2007

In this paper we investigate existence and multiplicity of solutions, with prescribed nodal properties, to a two-point boundary value problem of asymptotically linear $n$-th order equations. The proof follows a shooting approach and it is based on the weighted eigenvalue theory for linear $n$-th order boundary value problems

Multiplicity of ground states for the scalar curvature equation

2019

We study existence and multiplicity of radial ground states for the scalar curvature equation $$\begin{aligned} \Delta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n, \quad n>2, \end{aligned}$$when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ is bounded above and below by two positive constants, i.e. $$0 0$$, it is decreasing in (0, 1) and increasing in $$(1,+\infty )$$. Chen and Lin (Commun Partial Differ Equ 24:785–799, 1999) had shown the existence of a large number of bubble tower solutions if K is a sufficiently small perturbation of a positive constant. Our main purpose is to improve such a result by considering a non-perturbative situation: we ar…

Multiplicity of Radial Ground States for the Scalar Curvature Equation Without Reciprocal Symmetry

2022

AbstractWe study existence and multiplicity of positive ground states for the scalar curvature equation $$\begin{aligned} \varDelta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n\,, \quad n>2, \end{aligned}$$ Δ u + K ( | x | ) u n + 2 n - 2 = 0 , x ∈ R n , n > 2 , when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ K : R + → R + is bounded above and below by two positive constants, i.e. $$0<\underline{K} \le K(r) \le \overline{K}$$ 0 < K ̲ ≤ K ( r ) ≤ K ¯ for every $$r > 0$$ r > 0 , it is decreasing in $$(0,{{{\mathcal {R}}}})$$ ( 0 , R ) and increasing in $$({{{\mathcal {R}}}},+\infty )$$ ( R , + ∞ ) for a certain $${{{\mathcal {R}}}}&g…

Radial solutions of Dirichlet problems with concave-convex nonlinearities

2011

Abstract We prove the existence of a double infinite sequence of radial solutions for a Dirichlet concave–convex problem associated with an elliptic equation in a ball of R n . We are interested in relaxing the classical positivity condition on the weights, by allowing the weights to vanish. The idea is to develop a topological method and to use the concept of rotation number. The solutions are characterized by their nodal properties.