An anti-maximum principle for linear elliptic equations with an indefinite weight function

Anti-maximum Principles for Indefinite-weight Elliptic Problems

λ0 = λ0(1, P, Ω) := sup{λ ∈ R : ∃u > 0 s.t. (P − λ)u ≥ 0 in Ω}, where 1 is the constant function on Ω, taking at any point x ∈ Ω the value 1. Using the Krein-Rutman theorem, the author proved in [13, 14] generalized maximum principles and anti-maximum principles (in brief, GMPs and AMPs, respectively) for the problem (P − λ)uλ = f 0 in Ω. (1.1) In particular, these GMPs and AMPs (without weight...

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

A maximum principle for linear elliptic systems with discontinuous coefficients

We prove a maximum principle for linear second order elliptic systems in divergence form with discontinuous coefficients under a suitable condition on the dispersion of the eigenvalues of the coefficients matrix.

New Maximum Principles for Linear Elliptic Equations

We prove extensions of the estimates of Aleksandrov and Bakel′man for linear elliptic operators in Euclidean space R to inhomogeneous terms in L spaces for q < n. Our estimates depend on restrictions on the ellipticity of the operators determined by certain subcones of the positive cone. We also consider some applications to local pointwise and L estimates.

Bifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations

In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...