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Wellposedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data
Two sequences of solutions for indefinite superlinearsublinear elliptic equations with nonlinear boundary conditions
1.  Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 8408502, Japan 
2.  Department of Mathematics, Graduate School of Science, Osaka City University, 33138 Sugimoto Sumiyoshiku, Osakashi, Osaka, 5588585, Japan 
References:
[1] 
A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349381. Google Scholar 
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T. Bartsch and M. Willem, On an elliptic equation with concave and convex nonlinearities, Proc. Amer. Math. Soc., 123 (1995), 35553561. doi: 10.2307/2161107. Google Scholar 
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D. C. Clark, A variant of the LusternikSchnirelman theory, Indiana Univ. Math. J., 22 (1972), 6574. Google Scholar 
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D. G. DeFigueiredo, J.P. Gossez and P. Ubilla, Local superlinearity and sublinearity for indefinite semilinear elliptic problems, J. Funct. Anal., 199 (2003), 452467. doi: 10.1016/S00221236(02)000605. Google Scholar 
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D. G. DeFigueiredo, J.P. Gossez and P. Ubilla, Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity, J. Eur. Math. Soc., 8 (2006), 269288. doi: 10.4171/JEMS/52. Google Scholar 
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J. GarciaAzorero, I. Peral and J. D. Rossi, A convexconcave problem with a nonlinear boundary condition, J. Differential Equations, 198 (2004), 91128. doi: 10.1016/S00220396(03)000688. Google Scholar 
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R. Kajikiya, A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations, J. Funct. Anal., 225 (2005), 352370. doi: 10.1016/j.jfa.2005.04.005. Google Scholar 
[9] 
R. Kajikiya, Superlinear elliptic equations with singular coefficients on the boundary, Nonlinear Analysis, T.M.A., 73 (2010), 21172131. doi: 10.1016/j.na.2010.05.039. Google Scholar 
[10] 
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, translated by Scripta Technica, Inc. Mathematics in Science and Engineering, Vol. 46, Academic Press, 1968. Google Scholar 
[11] 
D. Naimen, Existence of infinitely many solutions for nonlinear Neumann problems with indefinite coefficients,, Submitted for publications., (). Google Scholar 
[12] 
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics Vol. 65, American Mathematical Society, Providence, RI, 1986. Google Scholar 
[13] 
M. Struwe, Variational Methods, 2nd edition, Springer, Berlin, 1996. Google Scholar 
[14] 
Z.Q. Wang, Nonlinear boundary value problems with concave nonlinearities near the origin, Nonlinear Differential Equations Appl., 8 (2001), 1533. doi: 10.1007/PL00001436. Google Scholar 
show all references
References:
[1] 
A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349381. Google Scholar 
[2] 
A. Ambrosetti, H. Brezis and G. Cerami, Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 122 (1994), 519543. doi: 10.1006/jfan.1994.1078. Google Scholar 
[3] 
T. Bartsch and M. Willem, On an elliptic equation with concave and convex nonlinearities, Proc. Amer. Math. Soc., 123 (1995), 35553561. doi: 10.2307/2161107. Google Scholar 
[4] 
D. C. Clark, A variant of the LusternikSchnirelman theory, Indiana Univ. Math. J., 22 (1972), 6574. Google Scholar 
[5] 
D. G. DeFigueiredo, J.P. Gossez and P. Ubilla, Local superlinearity and sublinearity for indefinite semilinear elliptic problems, J. Funct. Anal., 199 (2003), 452467. doi: 10.1016/S00221236(02)000605. Google Scholar 
[6] 
D. G. DeFigueiredo, J.P. Gossez and P. Ubilla, Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity, J. Eur. Math. Soc., 8 (2006), 269288. doi: 10.4171/JEMS/52. Google Scholar 
[7] 
J. GarciaAzorero, I. Peral and J. D. Rossi, A convexconcave problem with a nonlinear boundary condition, J. Differential Equations, 198 (2004), 91128. doi: 10.1016/S00220396(03)000688. Google Scholar 
[8] 
R. Kajikiya, A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations, J. Funct. Anal., 225 (2005), 352370. doi: 10.1016/j.jfa.2005.04.005. Google Scholar 
[9] 
R. Kajikiya, Superlinear elliptic equations with singular coefficients on the boundary, Nonlinear Analysis, T.M.A., 73 (2010), 21172131. doi: 10.1016/j.na.2010.05.039. Google Scholar 
[10] 
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, translated by Scripta Technica, Inc. Mathematics in Science and Engineering, Vol. 46, Academic Press, 1968. Google Scholar 
[11] 
D. Naimen, Existence of infinitely many solutions for nonlinear Neumann problems with indefinite coefficients,, Submitted for publications., (). Google Scholar 
[12] 
P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics Vol. 65, American Mathematical Society, Providence, RI, 1986. Google Scholar 
[13] 
M. Struwe, Variational Methods, 2nd edition, Springer, Berlin, 1996. Google Scholar 
[14] 
Z.Q. Wang, Nonlinear boundary value problems with concave nonlinearities near the origin, Nonlinear Differential Equations Appl., 8 (2001), 1533. doi: 10.1007/PL00001436. Google Scholar 
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