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Let Ω be a bounded domain in $ℝ^{N}$ with smooth boundary. Consider the following elliptic system: $- Δ u = \partial_{v} H (u, v, x)$ in Ω, $- Δ v = \partial_{u} H (u, v, x)$ in Ω, u = 0, v = 0 in ∂Ω. (ES) We assume that H is an even "-"-type Hamiltonian function whose first order partial derivatives satisfy appropriate growth conditions. We show that if (0,0) is a hyperbolic solution of (ES), then (ES) has at least 2|μ| nontrivial solutions, where μ = μ(0,0) is the renormalized Morse index of (0,0). This proves a conjecture by Angenent and van der Vorst.

A survey of recent progress on the multiplicity and stability problems for closed geodesics on Finsler 2-spheres is given.

Multiplicity of positive and nodal solutions for nonhomogeneous elliptic problems in unbounded cylinder domains.

Hsu, Tsing-San (2009)

Boundary Value Problems [electronic only]

Multiplicity of positive solutions of nonlinear elliptic equations with critical sobolev exponent in some contractible domains.

Donato Passaseo (1989)

Manuscripta mathematica

Multiplicity results for $p$ -sublinear $p$ -Laplacian problems involving indefinite eigenvalue problems via Morse theory.

Perera, Kanishka, Agarwal, Ravi P., O'Regan, Donal (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Multiple periodic solutions for a class of second-order nonlinear neutral delay equations.

Multiple periodic solutions to a class of second-order nonlinear mixed-type functional differential equations.

Multiple positive solutions for a critical quasilinear equation via Morse theory

Multiple positive solutions for a p-Laplace critical problem (p >1), via Morse theory

Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities.

Multiple semiclassical states for singular magnetic nonlinear Schrödinger equations.

Multiple solutions for nonlinear elliptic equations on Riemannian manifolds.

Multiple solutions for the $p$ -Laplace equation with nonlinear boundary conditions.

Multiple Solutions of Differential Equations Without the Palais-Smale Condition.

Multiple solutions of indefinite elliptic systems via a Galerkin-type Conley index theory

Multiple solutions of supercritical elliptic problems in perturbed domains

Multiple solutions of the forced double pendulum equation

Multiple solutions to some singular nonlinear Schrödinger equations.

Multiplicity and stability of closed geodesics on Finsler 2-spheres

Multiplicity of positive and nodal solutions for nonhomogeneous elliptic problems in unbounded cylinder domains.

Multiplicity of positive solutions of nonlinear elliptic equations with critical sobolev exponent in some contractible domains.

Multiplicity of solutions for a class of elliptic systems in $ℝ^{N}$ .

Multiplicity of solutions for gradient systems using Landesman-Lazer conditions.

Multiplicity results for nonlinear elliptic equations.

Multiplicity results for $p$ -sublinear $p$ -Laplacian problems involving indefinite eigenvalue problems via Morse theory.

Currently displaying 21 – 40 of 41