In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/(N-2) is the critical Sobolev exponent, 2 < q < 2 , 0≤μ < μˉ=(N-2)2_4 , a(x), k(x) ∈ C(RN ). Through a compactne...In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/(N-2) is the critical Sobolev exponent, 2 < q < 2 , 0≤μ < μˉ=(N-2)2_4 , a(x), k(x) ∈ C(RN ). Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a(x) and k(x).展开更多
This paper is concerned with the bounded value problems1/p（t）（p（t）u’）’+f（u）=0, t】0, u’（0）=0, lim t→+∞ u（t）=0,where f（0）=0. Such problems arise in the study of semi-linear elliptic differential equa...This paper is concerned with the bounded value problems1/p（t）（p（t）u’）’+f（u）=0, t】0, u’（0）=0, lim t→+∞ u（t）=0,where f（0）=0. Such problems arise in the study of semi-linear elliptic differential equa-tions in R<sup>n</sup>. It is shown that the problem has at most one positive solution under appro-priate conditions on f and p. Our result can include the important case that p（t）=f<sup>n-1</sup>and f（u）=u<sup>P</sup>-u, where n】1, p】1 are some given constants.展开更多
We consider the quasilinear Schrdinger equations of the form-ε~2?u + V(x)u- ε~2?(u2)u = g(u), x ∈ R^N,where ε > 0 is a small parameter, the nonlinearity g(u) ∈ C^1(R) is an odd function with subcritical growth...We consider the quasilinear Schrdinger equations of the form-ε~2?u + V(x)u- ε~2?(u2)u = g(u), x ∈ R^N,where ε > 0 is a small parameter, the nonlinearity g(u) ∈ C^1(R) is an odd function with subcritical growth and V(x) is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV(x) <inf ?ΛV(x) for some open bounded subset Λ of RN. We prove that there is an ε0 > 0 such that for all ε∈(0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V(x) as ε→ 0^+.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10631030, 10871075)the PhD Specialized Grant of the Ministry of Education of China (Grant No. 20060511001)the Natural Science Foundation of Guangdong Province, China (Grant No. 9451064201003736)
文摘In this paper, we are concerned with the following class of elliptic problems:where 2 = 2N/(N-2) is the critical Sobolev exponent, 2 < q < 2 , 0≤μ < μˉ=(N-2)2_4 , a(x), k(x) ∈ C(RN ). Through a compactness analysis of the functional corresponding to the problems , we obtain the existence of positive solutions for this problem under certain assumptions on a(x) and k(x).
基金This work was partially supported by Institute of Mathematics,Academia Sinica.
文摘This paper is concerned with the bounded value problems1/p（t）（p（t）u’）’+f（u）=0, t】0, u’（0）=0, lim t→+∞ u（t）=0,where f（0）=0. Such problems arise in the study of semi-linear elliptic differential equa-tions in R<sup>n</sup>. It is shown that the problem has at most one positive solution under appro-priate conditions on f and p. Our result can include the important case that p（t）=f<sup>n-1</sup>and f（u）=u<sup>P</sup>-u, where n】1, p】1 are some given constants.
基金supported by National Natural Science Foundation of China(Grant Nos.11371160 and 11328101)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.#IRT13066)
文摘We consider the quasilinear Schrdinger equations of the form-ε~2?u + V(x)u- ε~2?(u2)u = g(u), x ∈ R^N,where ε > 0 is a small parameter, the nonlinearity g(u) ∈ C^1(R) is an odd function with subcritical growth and V(x) is a positive Hlder continuous function which is bounded from below, away from zero, and infΛV(x) <inf ?ΛV(x) for some open bounded subset Λ of RN. We prove that there is an ε0 > 0 such that for all ε∈(0, ε0],the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V(x) as ε→ 0^+.
