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41.
Existence of solutions to a class of nonlinear second order two-point boundary value problems 总被引:2,自引:0,他引:2
Fuyi Li Zhanping Liang Qi Zhang 《Journal of Mathematical Analysis and Applications》2005,312(1):357-373
In this paper, the existence and multiplicity results of solutions are obtained for the second order two-point boundary value problem −u″(t)=f(t,u(t)) for all t∈[0,1] subject to u(0)=u′(1)=0, where f is continuous. The monotone operator theory and critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator and its properties play an important role. 相似文献
42.
Michael?Filippakis Leszek?Gasiński Nikolaos?S.?PapageorgiouEmail author 《Journal of Global Optimization》2005,31(1):173-189
We study nonlinear elliptic problems driven by the p-Laplacian and with a nonsmooth locally Lipschitz potential (hemivariational inequality). We do not assume that the nonsmooth potential satisfies the Ambrosetti--Rabinowitz condition. Using a variational approach based on the nonsmooth critical point theory, we establish the existence of at least one smooth positive solution.Mathematics Subject Classifications (2000). 35J50, 35J85, 35R70.This article is Revised version.Leszek Gasiski is an award holder of the NATO Science FellowshipProgramme, which was spent in the National Technical University of Athens. 相似文献
43.
Sophia Th.?Kyritsi Nikolaos S.?PapageorgiouEmail author 《Annali di Matematica Pura ed Applicata》2005,184(4):449-472
In this paper we examine a nonlinear elliptic problem driven by the p-Laplacian differential operator and with a potential function which is only locally Lipschitz, not necessarily C1 (hemivariational inequality). Using the nonsmooth critical point theory of Chang, we obtain two strictly positive solutions.
One solution is obtained by minimization of a suitable modification of the energy functional. The second solution is obtained
by generalizing a result of Brezis-Nirenberg about the local C10-minimizers versus the local H10-minimizers of a C1-functional.
Mathematics Subject Classification (2000) 35J50, 35J85, 35R70 相似文献
44.
Critical point theory is used to show the existence of weak solutions to a quasilinear elliptic differential equation under the functional framework of the Musielak–Sobolev spaces in a bounded smooth domain with Dirichlet boundary condition. 相似文献
45.
樊自安 《数学的实践与认识》2017,(11):247-254
讨论了一类包含次临界和临界Sobolev指数的Schr(o)dinger-Possion方程解的存在性.应用Nehari流形和变分方法,在不同情况下,得到了方程至少存在一个解. 相似文献
46.
Using a change of variables, we convert a quasilinear elliptic equation into a semilinear one. Then by Jeanjean?s result [6], we get a bounded (PS) sequence for the corresponding functional and show the existence of positive nontrivial solution. 相似文献
47.
In this paper we study an indefinite Kirchhoff type equation with steep potential well. Under some suitable conditions, the existence and the non-existence of nontrivial solutions are obtained by using variational methods. Furthermore, the phenomenon of concentration of solutions is also explored. 相似文献
48.
49.
Zigao Chen 《Annals of Differential Equations》2014,(3):272-281
In this paper, we consider a p(x)-biharmonic problem with Navier boundary conditions. The existence of infinitely many solutions which tend to zero is investigated based on the symmetric Mountain Pass lemma. Our approach relies on the theory of variable exponent Sobolev space. 相似文献
50.
This article deals with the problem where n = p. The authors prove that a Hardy inequality and the constant (p/p-1)p is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma. 相似文献