Remark on solvability of p-Laplacian equations in large dimension
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G. Aronsson, Representation of a p-harmonic function near a critical point in the plane, Manuscripta Mathematica 66 (1989), 73–95.
J. García Azorero and I. Peral, On an Emden-Fowler type equation, Nonlinear Analysis T.M.A. 18 (1992), 1085–1097.
J. García Azorero and I. Peral, Existence and nonuniqueness for the p-Laplacian: nonlinear eigenvalues, Communications in Partial Differential Equations 12 (1987), 1389–1430.
J. García Azorero, I. Peral and J. P. Puel, Quasilinear problems with exponential growth in the reaction term, Nonlinear Analysis T.M.A. 22 (1994), 481–498.
X. Cabré and M. Sanchón, Semi-stable and extremal solutions of reaction equations involving the p-Laplacian, Communications in Pure and Applied Analysis 6 (2007), 43–67.
E. DiBenedetto, C 1+αlocal regularity of weak solutions of degenerate elliptic equations, Nonlinear Analysis 7 (1983), 827–850.
A. Ferrero, On the solutions of quasilinear elliptic equations with a polynomial-type reaction term, Advances in Differential Equations 9 (2004), 1201–1234.
P. Girg and M. Chhetri, Superhomogeneous semipositone problem for the p-Laplacian, in The Sixth Mississippi State-UAB Conference on Differential Equations & Computer Simulaions, May 13–14, 2005, Mississippi State University, Mississippi State, USA.
T. Iwaniec and J. Manfredi, Regularity of p harmonic functions on the plane, Revista Matemática Iberoamericana 5 (1989), 1–19.
O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968.
Y. V. Lakshmikantham, Hölder continuity of the inverse of p-Laplacian, Journal of Mathematical Analysis and Applications 221 (1998), 734–748.
J. Lewis, Regularity of the derivatives of solutions to certain elliptic equations, Indiana University Mathematics Journal 32 (1983), 849–858.
G. M. Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Analysis 12 (1988), 1203–1219.
P. Lindqvist, Addendum: “On the equation div(|∇u| p-2∇u) + λ|u| p-2u = 0”, (Proceedings of the American Mathematical Society 109 (1990), 157–164), Proceedings of the American Mathematical Society 16 (1992), 583-584.
J. L. Lions, Quelques Méthodes de Résolution des Probl`emes aux Limites non Linéaire, Dunod et Gauthier-Villars, Paris, 1969.
I. Peral, Multiplicity of Solutions for the p-Laplacian, Miramare Trieste, Italy, 1997.
S. I. Pohozaev, On the eigenfunctions of the equation Δu + λf(u) = 0, Soviet Mathematics-Doklady 6 (1965), 1408–1411.
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, 1986.
J. Serrin, Local behavior of solutions of quasi-linear elliptic equations, Acta Mathematica 111 (1964), 247–302.
P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, Journal of Differential Equations 51 (1984), 126–150.
K. Uhlenbeck, Regularity for a class of non-linear elliptic systems, Acta Mathematica 138 (1977), 219–240.
O. Zubelevich, Solvability of quasilinear elliptic equations in large dimensions, Electronic Journal of Differential Equations 101 (2005), 1–4.