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Multiple positive solutions of nonhomogeneous semilinear elliptic equations in N*

  • Cao Dao-Min (a1) and Zhou Huan-Song (a1)
Abstract

We consider the following problem

where for all ≦f(x,u)≦c1up-1 + c2u for all x ∈ℝN,u≧0 with c1>0,c2∈(0, 1), 2<p<(2N/(N – 2)) if N ≧ 3, 2 ≧ + ∝ if N = 2. We prove that (*) has at least two positive solutions if

and h≩0 in ℝN, where S is the best Sobolev constant and

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5W. Y. Ding and W. M. Ni . On the existence of entire solution of a semilinear elliptic equation. Arch. Rational Meek Anal. 91 (1986). 283308.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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