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# Abstract. We find for small ε positive solutions to the equation

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(1)

−2a

2(1+a)

p−1

bp

N

N

N

N

(2)

N

N

N

N−2−2a2

j

(3)

1,2a

N

2p

a1,2

N

1

(4)

2

2

a1,2

N

N

N

N

N

N

N

N−2−2a2

1,2

λ

(5)

N

N

N

N

N

N

N

N−2−2a2

## #

N−2(1+a−b)4(1+a−b)

N−2(1+a−b)2(1+a

−b)

(6)

## #

N−2(1+a−b)4(1+a−b)

## |x|

### √

(N−2−2a)2−4λ N−2−2a

### 

(N−2−2a)(1+a−b) N−2(1+a−b)

## 1 + |x|

2(1+a−b)

### √

(N−2−2a)2−4λ N−2(1+a−b)

## # −

N2(1+a−2(1+a−b)−b)

N−2−2a2

a,b,λ

µ

N−1

N−1

(7)

(8)

N

N

N

N

N

N

N

N

p−2p

N

(9)

D1,2 a,λ(RN )

N

D1,2 a,λ

N

N

p−1p

p−1p

N

p−1p

p−1p

p−1p

p−1p

p−1p

p−1p

p−2p

p−2p

p−2

N−2−2a2

−1

(10)

µ

µ

1

1

z1

z

1

2

N

1

2

N

N

µ

µ

(11)

−1

(12)

0

0

0

0

0

0

p1

−2

µ

0

1

µ

µ

µ

ε

ε

(13)

−1

ε

ε

N

N

N

N

N

N

N

N

(14)

N

N

N

N

N

N

r

+

(15)

## [12] S. Terracini. On positive entire solutions to a class of equations with a singular coeffi- cient and critical exponent . Adv. Differential Equations, 1 (1996), no. 2, 241–264.

### E-mail address: schneid@sissa.it, felli@sissa.it

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