## Differential and Integral Equations

- Differential Integral Equations
- Volume 18, Number 7 (2005), 721-764.

### Positive solution branch for elliptic problems with critical indefinite nonlinearity

Jacques Giacomoni, J. Prajapat, and Mythily Ramaswamy

#### Abstract

In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $- \Delta u =\lambda u + h (x) u^{\frac{n+2}{n-2}} $ in a smooth domain bounded (respectively, unbounded) $\Omega\subseteq\,\mathbb R^n , \ n > 4 $, for $\lambda \geq 0 $. Under suitable assumptions on the weight function, we obtain the positive solution branch, bifurcating from the first eigenvalue $\lambda_1(\Omega)$ (respectively, the bottom of the essential spectrum).

#### Article information

**Source**

Differential Integral Equations, Volume 18, Number 7 (2005), 721-764.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060164

**Mathematical Reviews number (MathSciNet)**

MR2150656

**Zentralblatt MATH identifier**

1212.35091

**Subjects**

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations

Secondary: 35B33: Critical exponents 35J25: Boundary value problems for second-order elliptic equations 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

#### Citation

Giacomoni, Jacques; Prajapat, J.; Ramaswamy, Mythily. Positive solution branch for elliptic problems with critical indefinite nonlinearity. Differential Integral Equations 18 (2005), no. 7, 721--764. https://projecteuclid.org/euclid.die/1356060164