Rocky Mountain Journal of Mathematics

Multiplicity Results for a Semi-Linear Elliptic Equation Involving Sign-Changing Weight Function

Tsung-Fang Wu

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Rocky Mountain J. Math., Volume 39, Number 3 (2009), 995-1011.

First available in Project Euclid: 18 May 2009

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Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations

Semi-linear elliptic equations Nehari manifold concaveconvex nonlinearities


Wu, Tsung-Fang. Multiplicity Results for a Semi-Linear Elliptic Equation Involving Sign-Changing Weight Function. Rocky Mountain J. Math. 39 (2009), no. 3, 995--1011. doi:10.1216/RMJ-2009-39-3-995.

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  • A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), 519-543.
  • K.J. Brown and Y. Zhang, The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function, J. Diff. Equations 193 (2003), 481-499.
  • I. Ekeland, On the variational principle, J. Math. Anal. Appl. 17 (1974), 324-353.
  • D.G. de Figueiredo, J.P. Gossez and P. Ubilla, Local superlinearity and sublinearity for indefinite semilinear elliptic problems, J. Funct. Anal. 199 (2003), 452-467.
  • W.M. Ni and I. Takagi, On the shape of least energy solution to a Neumann problem, Comm. Pure Appl. Math. 44 (1991), 819-851.
  • P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, Regional Conference Series Math., American Mathematical Society, 1986.
  • G. Tarantello, On nonhomogeneous elliptic involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Lineairé 9% (1992), 281-304.
  • T.F. Wu, On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function, J. Math. Anal. Appl. 318 (2006), 253-270.