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Multiple positive solutions of nonhomogeneous semilinear elliptic equations in ℝ N

Cao Dao-Min, Zhou Huan-Song

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Source: Crossref

Published: Jan 1, 1996

DOI: 10.1017/s0308210500022836

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Source abstract

We consider the following problem where for all ≦ f(x,u)≦c 1 u p-1 + c 2 u for all x ∈ℝ N ,u≧0 with c 1 >0,c 2 ∈(0, 1), 2<p<(2 N/(N – 2)) if N ≧ 3, 2 ≧ + ∝ if N = 2. We prove that (*) has at least two positive solutions if and h≩0 in ℝ N , where S is the best Sobolev constant and

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Multiple positive solutions of nonhomogeneous semilinear elliptic equations in ℝ N — Mathematical Frontier Network