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http://dx.doi.org/10.7858/eamj.2014.024

MULTIPLE EXISTENCE OF POSITIVE GLOBAL SOLUTIONS FOR PARAMETERIZED NONHOMOGENEOUS ELLIPTIC EQUATIONS INVOLVING CRITICAL EXPONENTS  

Kim, Wan Se (Department of Mathematics, Research Institute for Natural Sciences, Hanyang University)
Publication Information
East Asian mathematical journal / v.30, no.3, 2014 , pp. 335-353 More about this Journal
Abstract
We establish multiple extence of positive solutions for parameterized nonhomogeneous elliptic equations involving critical Sobolev exponent. The approach to the problem is variational method.
Keywords
elliptic equations; critical exponents; bifurcation; multiplicity; positive solutions; super-sub subsolution; mountain pass lemma;
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1 P.L. Lions, The concentration-compactness principle in the calculus of variations, the locally compact case. part 2, Ann. Inst. H. Poincare Analyse non Lineaire, 1(4)(1984), 223-283,.   DOI
2 N. Hirano and W. S. Kim, Multiple existence of solutions for a nonhomogeneous elliptic problem on $\mathbb{R}^N$, Nonlinear Analysis. T.M.A., 74,(2011), 4369-4378.   DOI   ScienceOn
3 M. K. Kwong, Uniqueness of positive solution of ${\Delta}u- u+u^p=0\;in\;R^N$, Arch. Retional Mech. Anal. 105(3), (1989), 243-266.
4 P.L. Lions, The concentration-compactness principle in the calculus of variations, the locally compact case. part 1, Ann. Inst. H. Poincare Analyse non Lineaire, 1(2)(1984), 109-145,.   DOI
5 W.A. Strauss, Existence of solatary waves in higher dimensions, Communs. Math. Phys., 55(1977), 149-162.   DOI   ScienceOn
6 M. Willem, Minimax theorems, Birkhauser. Boston, Basel, Berlin. (1996).
7 X.-P. Zhu, Multiple entire solutions of a semilinear elliptic equation, Nonlinear analysis T.M.A., 12(11) (1988), 1297-1316.   DOI   ScienceOn
8 X.-P. Zhu, A perturbation result on positive entire solutions of a semilinear elliptic equation, J. Diff. Equa, 92 (1991) 163-178.   DOI
9 X.-P. Zhu, and H.-S. Zhu, Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domain , Proc. Roy. Soc. Edinburgh , 115 A (1990) 301-318.
10 A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funt. Anal., 14 (1973), 349-381.   DOI
11 S. Bae, Positive global solutions of inhomogenuous semilinear elliptic equations with critical sobolev exponent, Preprint.
12 H. Brezis and E. Lieb, A relation between pointwise convergence of functionals and convergence of functions,, Proc. Amer. Soc., 88 (1983), 486-490.   DOI
13 D.-M. Cao, Positive solutions and bifurcation from the essential spectrum of a semilinear elliptic equations on $\mathbb{R}^N$, Nonlinear Anal. T.M.A., 15(1990), 1048-1052.
14 Y. Deng and Li. Y, Existence and bifurcation of positive solutions for a semilinear elliptic equation with critical exponent, J. Diff. Equa., 130 (1996), 179-200.   DOI   ScienceOn
15 Y. Deng and Li. Y, Existence of multiple positive solutions for a semilinear elliptic equation, Adv. Differential Equations, 2(1997), 361-382.
16 W.-Y. Ding and W.-M. Ni On the existence of positive solutions for a semilinear elliptic equation, Archs Ration Mech. Analysis, 91(1986), 283-307.   DOI
17 L. Ekeland, Convex minimization problem, Bull. Amer. Math. Soc., (NS)1 (1976), 443-474.
18 L. Caffarely, G. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math 42(1986), 271-1191.
19 N. Hirano and W. S. Kim, Multiple existence of solutions for a nonhomogeneous elliptic problem with critical exponent on $\mathbb{R}^N$, J. Diff. Equa, 249,(2010), 1799-1816.   DOI   ScienceOn
20 N. Hirano, Existence of entire positive solutions for nonhomogeneous elliptic equations, Nonlinear Analysis. T.M.A., 29(8) (1997), 889-901.   DOI   ScienceOn
21 N. Hirano, Multiple existence of solutions for a nonhomogeneous elliptic problems on $\mathbb{R}^N$, J. Math. Anal. Appl., 336 (2007), 506-522.   DOI   ScienceOn
22 H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponent, Comm. Pure Appl. Math., 36 (1983), 437-427.   DOI