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Multiple existence of solutions for a nonhomogeneous ellpitic problems on $R^N$

Norimichi Hirano|김완세
영남수학회 (Youngnam Mathematical Society)|2018.09|East Asian Mathematical Journal|제34권 제5호|pp. 703-713|DOI http://dx.doi.org/10.7858/eamj.2018.049

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키워드

Positive solutionsSemilinear Elliptic problemEntire solutions.
주제분류수학

초록

Let N ≥ 3, 2∗ = 2N/(N −2) and p ∈ (2,2∗). Our purpose in this paper is to consider multiple existence of solutions of problem−∆u− μ +αu = |u|p−2u+λf u∈H1 RN , |x|2where a, λ > 0, μ ∈ 0, (N − 2)2/4 f ∈ H−1 RN , f ≥ 0 and f ̸≡ 0.

Abstract

Let N ≥ 3, 2∗ = 2N/(N −2) and p ∈ (2,2∗). Our purpose in this paper is to consider multiple existence of solutions of problem−∆u− μ +αu = |u|p−2u+λf u∈H1 RN , |x|2where a, λ > 0, μ ∈ 0, (N − 2)2/4 f ∈ H−1 RN , f ≥ 0 and f ̸≡ 0.

참고문헌 (10)

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  4. T. Bartsch, "Three nodal solutions of singularly perturbed elliptic equations on domain without topology", Ann. Inst. H. Poincare Anal. Non Lineaire, 22, pp.259~281 (2005)[DOI]
  5. D. Cao, "Multiple Positive Solutions of for an inhomogeneous semilinear elliptic equation in <TEX>$R^n$<", TEX>, 1996, pp.126, 443~464
  6. G. Cerami, "The effect of concentrating potentials in some sigularly perturbed problems", Calc. Var., 17, pp.257~281 (2003)
  7. "An inhomogeneous semilinear equation in entire space", J. Differential Equations, 125, pp.184~214 (1996)[DOI]
  8. Y. Deng, "Existence of multiple positive solutions for a semilinear elliptic equation", Advances in Differential Equations, 2, pp.361~382 (1997)
  9. N. Hirano, "Existence of entire positive solutions for non homogeneous elliptic equations", Nonlinear Analysis TMA, 29, pp.889~901 (1997)[DOI]
  10. X. Zhu, "A Perturbation result on positive entire solutions of a semilinear elliptic equation", J. Diff. Equations, 92, pp.163~178 (1991)[DOI]

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