An elliptic equation with perturbed p-Laplace operator

We consider an elliptic boundary value problem with perturbed p-Laplacian, p>1. The perturbation consists of a linear operator that dilates or compresses the argument of a function and is close to the identity. A weak existence theorem is obtained.     

An inverse problem for an elliptic equation with an affine term

We consider the following elliptic boundary value problem: on , u = 0 on where is a smooth bounded planar domain. We show that for a large class of domains and for any such that is not identically constant there exist at most finitely many different pairs of coefficients such that the problem has a solution with the normal flux on . Received: 4 February 1999     

An elliptic non-linear equation on a Riemann surface

New existence and uniqueness results for a second order elliptic non-linear equation are obtained by using gauge theory methods on linear holomorphic bundles over an oriented Riemann surface.     

On non-linear elliptic equation with weight

In this paper, we prove the existence and uniqueness theorem of the Dirichlet problem for certain non-linear elliptic operators with Muckenhoupt weight.     

A semilinear elliptic equation with double resonance

In this paper, the existence and multiplicity of a class of double resonant semilinear elliptic equations with the Dirichlet boundary value are studied.     

An elliptic equation under the effect of two nonlocal terms

The aim of this note is to investigate the existence of signed and sign‐changing solutions to the Kirchhoff type problem (0.1) where Ω is a bounded smooth domain in (N = 1,2,3), a,b > 0 and 2 < p < 2^?, with 2^?=+∞ if N = 1,2 and 2^?=6 if N = 3. Using variational methods, we show that (0.1) possesses three solutions of mountain pass type (one positive, one negative and one sign‐changing) and infinitely many high‐energy sign‐changing solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

On a semilinear elliptic equation with inverse-square potential

We study the existence and nonexistence of solutions to a semilinear elliptic equation with inverse-square potential. The dividing line with respect to existence or nonexistence is given by a critical exponent, which depends on the strength of the potential.     

Two dimensional elliptic equation with critical nonlinear growth

We study the asymptotic behavior of solutions to a semilinear elliptic equation associated with the critical nonlinear growth in two dimensions.

where is a unit disk in and denotes a positive parameter. We show that for a radially symmetric solution of (1.1) satisfies

Moreover, by using the Pohozaev identity to the rescaled equation, we show that for any finite energy radially symmetric solutions to (1.1), there is a rescaled asymptotics such as

locally uniformly in . We also show some extensions of the above results for general two dimensional domains.

     

Solvability for nonlinear elliptic equation with boundary perturbation

The solvability of nonlinear elliptic equation with boundary perturbation is consid- ered.The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.     

An irregular complex valued solution to a scalar uniformly elliptic equation

We present an irregular weak solution of a uniformly elliptic scalar equation in divergence form with measurable coefficients. The solution has a square integrable gradient. Such examples have been known for dimension n ≥ 5 only. The author was partially supported by SFB 611.