Stability and intersection properties of solutions to the nonlinear biharmonic equation
نویسندگان
چکیده
منابع مشابه
Stability and Intersection Properties of Solutions to the Nonlinear Biharmonic Equation
We study the positive, regular, radially symmetric solutions to the nonlinear biharmonic equation ∆φ = φ. First, we show that there exists a critical value pc, depending on the space dimension, such that the solutions are linearly unstable if p < pc and linearly stable if p ≥ pc. Then, we focus on the supercritical case p ≥ pc and we show that the graphs of no two solutions intersect one another.
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In this note we use the Nehari manifold and fibering maps to show existence of positive solutions for a nonlinear biharmonic equation in a bounded smooth domain in Rn, when n = 5, 6, 7. Mathematics Subject Classification: 35J35, 35J40
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We present new singular solutions of the biharmonic nonlinear Schrödinger equation (NLS) iψt(t,x)− ψ + |ψ |2σψ = 0, x ∈ R , 4/d σ 4. These solutions collapse with the quasi-self-similar ring profile ψQB , where |ψQB(t, r)| ∼ 1 L2/σ (t) QB ( r − rmax(t) L(t) ) , r = |x|, L(t) is the ring width that vanishes at singularity, rmax(t) ∼ r0L(t) is the ring radius, and α = (4 − σ)/(σ (d − 1)). The blo...
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We consider singular solutions of the L 2-critical biharmonic nonlinear Schrödinger equation. We prove that the blowup rate is bounded by a quartic-root, the solution approaches a quasi–self-similar profile, and a finite amount of L 2-norm, which is no less than the critical power, concentrates into the singularity. We also prove the existence of a ground-state solution. We use asymptotic analy...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2009
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/22/7/009