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Original Articles

Positive solutions of indefinite equations with p-Laplacian and supercritical nonlinearity

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Pages 945-954 | Received 15 Sep 2010, Accepted 07 Mar 2011, Published online: 07 Jul 2011

References

  • Alama , S and Tarantello , G . 1993 . On semilinear elliptic problems with indefinite nonlinearities . Calc. Var. , 1 : 439 – 475 .
  • Berestycki , H , Capuzzo–Dolcetta , I and Nirenberg , L . 1994 . Superlinear indefinite elliptic problems and nonlinear Liouville theorem . Topol. Methods Nonlinear Anal. , 4 : 59 – 78 .
  • Ouyang , T . 1991 . On the positive solutions of semilinear equations Δu + λu + hu p  = 0 on compact manifolds. Part II . Indiana Univ. Math. J. , 40 : 1083 – 1141 .
  • Binding , PA , Drabek , P and Huang , YX . 1999 . Positive solutions of critical quasilinear elliptic equations in ℝ N . Math. Bohem. , 124 : 149 – 166 .
  • Drábek , P and Pohozaev , SI . 1997 . Positive solution for the p-Laplacian: Application of the fibering method . Proc. R. Soc. Edinb. Sect. A , 127 : 703 – 726 .
  • Egnell , H . 1988 . Existence and nonexistence results for m-Laplacian: Application of the fibering method . Arch. Ration. Mech. Anal. , 104 : 57 – 77 .
  • Kandilakis , DA and Lyberopoulos , AN . 2006 . Indefinite quasilinear elliptic problems with subcritical and supercritical nonlinearities on unbounded domains . J. Differ. Eqns , 230 : 337 – 361 .
  • Berestycki , H , Capuzzo–Dolcetta , I and Nirenberg , L . 1995 . Variational methods for indefinite superlinear homogeneous elliptic problems . NoDEA , 2 : 553 – 572 .
  • Del Pino , M . 1994 . Positive solutions of a semilinear elliptic equation on a compact manifold . Nonlinear Anal. , 22 : 1423 – 1430 .
  • Il'yasov , Y and Runst , T . 2005 . On nonlocal calculation for inhomogeneous indefinite Neumann boundary value problems . Calc. Var. , 22 : 101 – 127 .
  • Drábek , P , Elkhalil , A and Touzani , A . 1999 . A bifurcation problem for the principal eigencurve of the p-Laplacian . Appl. Anal. , 72 : 399 – 410 .
  • Il'yasov , Y . 2001 . On positive solutions of indefinite elliptic equations . C. R. Acad. Sci., Paris, Série I , 332 : 1 – 6 .
  • Il'yasov , Y . 2007 . Bifurcation calculus by the extended functional method . Funct. Anal. Appl. , 41 : 23 – 38 .
  • Krasnosel'skii , MA , Lifshits , JeA and Sobolev , AV . 1990 . Positive Linear Systems: The Method of Positive Operators , Berlin : Helderman Verlag .
  • Struwe , M . 1996 . Variational Methods, Application to Nonlinear Partial Differential Equations and Hamiltonian Systems , Berlin, Heidelberg, New York : Springer-Verlag .
  • Anane , A . 1987 . Simplicité et isolation de la première valeur propre du p-Laplacien avec poids . C. R. Acad. Sci., Paris, Sér. I , 305 : 725 – 728 .
  • Lindqvist , P . 1990 . On the equation . Proc. Am. Math. Soc. , 109 : 157 – 164 .
  • Lieberman , GM . 1988 . Boundary regularity for solutions of degenerate elliptic equations . Nonlinear Anal. , 12 : 1203 – 1219 .
  • Tolksdorf , P . 1984 . Regularity for a more general class of quasilinear elliptic equations . J. Differ. Eqns , 51 : 126 – 150 .
  • Vázquez , JL . 1984 . A strong maximum principle for some quasilinear elliptic equations . Appl. Math. Optim. , 12 : 191 – 202 .
  • Il'yasov , Y . 2002 . Nonlocal investigations of bifurcations for solutions of nonlinear elliptic equations . Izv. Russ. Ac. N. Ser. Mat. , 66 : 19 – 48 .
  • Pohozaev , SI . 1979 . On an approach to nonlinear equations . Dokl. Acad. Sci. USSR , 247 : 1327 – 1331 .
  • Pohozaev , SI . 1990 . On the method of fibering a solution in nonlinear boundary value problems . Proc. Stekl. Inst. Math. , 192 : 157 – 173 .
  • Il'yasov , Y . 1998 . On asymptotics of solutions to semilinear elliptic equations near the first eigenvalue of a nonperturbed problem . Mat. Notes , 64 : 471 – 475 .
  • Cabre , X and Sanchon , M . 2007 . Semi-stable and extremal solutions of reaction equations involving the p-Laplacian . J. Commun. Pure Appl. Anal. , 6 : 43 – 67 .

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