We study boundary blow-up solutions of semilinear elliptic equations Lu = up + with p > 1, or Lu = e with a > 0, where L is a second order elliptic operator with measurable coefficients. Several uniqueness theorems and an existence theorem are obtained.

We consider the existence and regularity of weakly polyharmonic almost complex structures on a compact Hermitian manifold $$M^{2m}$$ . Such objects satisfy elliptic system $$[\varDelta ^m J, J]=0$$ weakly. prove general theorem for semilinear systems in critical dimensions (with growth nonlinearities), which includes dimension four six.

In this paper we extend the idea of interpolated coefficients for semilinear problems to the finite volume element method based on rectangular partition. At first we introduce bilinear finite volume element method with interpolated coefficients for a boundary value problem of semilinear elliptic equation. Next we derive convergence estimate in H 1-norm and superconvergence of derivative. Finall...

We generalize previous uniqueness results on a semilinear elliptic equation with zero Dirichlet boundary condition and superlinear, subcritical nonlinearity. Our proof is based on a bifurcation approach and a Pohozaev type integral identity, which greatly simplifies the previous arguments.

We study the semilinear elliptic system ∆u = λp(x)f(v),∆v = λq(x)g(u), in an unbounded domain D in R2 with compact boundary subject to some Dirichlet conditions. We give existence results according to the monotonicity of the nonnegative continuous functions f and g. The potentials p and q are nonnegative and required to satisfy some hypotheses related on a Kato class.

We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function Σ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of Σ in the sense of subdifferential calcul...

We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter λ, we consider the system −∆v = λf(u) in Ω, −∆u = g(v) in Ω, u = v = 0 on ∂Ω, where Ω is a smooth bounded domain in R with N ≥ 1. One solution is obtained applying Ambrosetti and Rabinowitz’s classical Mountain Pass Theorem, and t...

In this paper, we study the asymptotic behavior of positive solutions and apply the “improved moving plane” method to prove the symmetry of positive solutions of semilinear elliptic systems in unbounded cylinders.

We establish a priori bounds for positive solutions of semilinear elliptic systems of the form 8><>>>: −∆u = g(x, v) , in Ω −∆v = f(x, u) , in Ω u > 0 , v > 0 in Ω

We obtain precise global bifurcation diagrams for both one-sign and sign-changing solutions of a semilinear elliptic equation, for the nonlinearity being asymptotically linear. Our method combines the bifurcation approach and spectral analysis.