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In this paper, we consider the Finsler-Liouville equation with homogeneous Dirichlet boundary condition on a smooth bounded domain Ω⊂R². We deal with existence issues by using variational approach when Ω has non-trivial topology. In particular, we generalize the Wang-Xia's results in [19]. [ABSTRACT FROM AUTHOR]

This paper investigates the positive solutions for second order linear elliptic equation in unbounded cylinder with zero boundary condition. We prove there exist two special positive solutions with exponential growth at one end while exponential decay at the other, and all the positive solutions are linear combinations of these two. [ABSTRACT FROM AUTHOR]

In this paper, using a geometric method we show that the blow-up values of the elliptic sinh-Gordon equation are multiples of 8 π. [ABSTRACT FROM AUTHOR]

Motivated by the supersymmetric extension of Liouville theory in the recent physics literature, we couple the standard Liouville functional with a spinor field term. The resulting functional is conformally invariant. We study geometric and analytic aspects of the resulting Euler-Lagrange equations, culminating in a blow up analysis. [ABSTRACT FROM AUTHOR]

We consider Liouville type problems of stable quasi-harmonic\linebreak maps, by ``stable'' we mean that the second variation of quasi-energy functional $E_q(u) $ is nonnegative, and we prove that the stable quasi-harmonic maps must be constant under some geometry conditions. [ABSTRACT FROM AUTHOR]

We adopt a continuous model to estimate the Grothendieck constants. An analytical formula to compute the lower bounds of Grothendieck constants has been explicitly derived for arbitrary orders, which improves previous bounds. Moreover, our lower bound of the Grothendieck constant of order three gives a refined bound of the threshold value for the nonlocality of the two-qubit Werner states. [ABSTRACT FROM AUTHOR]

We study the boundary value problem for the -- conformally invariant -- super-Liouville functional E(u,ψ)=∫M{12|∇u|2+Kgu+((D/+eu)ψ,ψ)-e2u}dz that couples a function u and a spinor ψ on a Riemann surface. The boundary condition that we identify (motivated by quantum field theory) couples a Neumann condition for u with a chirality condition for ψ. Associated to any solution of the super-Liouville system is a holomorphic quadratic differential T(z)T(z), and when our boundary condition is satisfied, T becomes real on the boundary. We provide a complete regularity and blow-up analysis for solutions of this boundary value problem. [ABSTRACT FROM AUTHOR]