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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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We study existence of positive solutions of the classical nonlinear Schr¨odinger equation [수식]In fact, we consider the following more general quasi-linear Schr¨odinger equation [수식]where m ∈ (1, n) is a positive number and [수식]is the corresponding critical Sobolev embedding number in Rn. Under appropriate conditions on the functions V (x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.
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참고문헌 (17)
참고문헌 신청
A. Ambrosetti / 1973 / Dual variational methods in critical point theory and applications / J. Functional Analysis 14 : 349 ~ 381
E. DiBenedetto / 1983 / C1+® local regularity of weak solutions of degenerate elliptic equations / Nonlinear Anal. 7 (8) : 827 ~ 850
G. Talenti / 1976 / Best constant in Sobolev inequality / Ann. Mat. Pura Appl. 110 : 353 ~ 372
H. Brezis / 1983 / Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents / Comm. Pure Appl. Math. 36 (4) : 437 ~ 477
J. Serrin / 1964 / Local behavior of solutions of quasi-linear equations / Acta Math. 111 : 247 ~ 302
E. DiBenedetto / 1983 / C1+® local regularity of weak solutions of degenerate elliptic equations / Nonlinear Anal. 7 (8) : 827 ~ 850
G. Talenti / 1976 / Best constant in Sobolev inequality / Ann. Mat. Pura Appl. 110 : 353 ~ 372
H. Brezis / 1983 / Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents / Comm. Pure Appl. Math. 36 (4) : 437 ~ 477
J. Serrin / 1964 / Local behavior of solutions of quasi-linear equations / Acta Math. 111 : 247 ~ 302
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