Sign-changing saddle point

SADDLE POINT VARIATIONAL METHOD FOR DIRAC CONFINEMENT

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...

Solutions for m-Point BVP with Sign Changing Nonlinearity

Hua Su School of Statistics and Mathematic, Shandong University of Finance, Jinan, Shandong 250014, China Correspondence should be addressed to Hua Su, [email protected] Received 24 October 2008; Accepted 31 January 2009 Recommended by Binggen Zhang We study the existence of positive solutions for the following nonlinear m-point boundary value problem for an increasing homeomorphism and homomorph...

Positive and Sign-changing Clusters around Saddle Points of the Potential for Nonlinear Elliptic Problems

We study the existence and asymptotic behavior of positive and sign-changing multipeak solutions for the equation −ε∆v + V (x)v = f(v) in R , where ε is a small positive parameter, f is a superlinear, subcritical and odd nonlinearity, V is a uniformly positive potential. No symmetry on V is assumed. It is known ([19]) that this equation has positive multipeak solutions with all peaks approachin...

Maxima to Saddle-point Problems

Saddle-Point Dynamics: Conditions for Asymptotic Stability of Saddle Points

This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics (gradient-descent in the first variable and gradientascent in the second one). We identify a suite of complementary conditions under which the set of saddle points is a...