共查询到20条相似文献,搜索用时 15 毫秒
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Mathematical Notes - For elliptic systems with discontinuous nonlinearities, we study the existence of strong solutions whose values are points of continuity with respect to the state variables for... 相似文献
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Hong-Kun Xu 《Applicable analysis》2013,92(2):179-199
The nonsmooth critical point theory is applied to prove the existence of solutions and multiple solutions of a quasilinear elliptic equation with discontinuous nonlinearities. 相似文献
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研究一类Klein-Gordon-Maxwell系统解的存在性和多重性.当非线性项是凹凸非线性项时,利用变分方法获得了系统解的存在性和多重性结果,并完善了此系统解的存在性的已有结果. 相似文献
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We consider the Dirichlet problem for an equation of the elliptic type with a nonlinearity discontinuous with respect to the phase variable in the resonance case; it is not required that the nonlinearity satisfy the Landesman-Lazer condition. Using the regularization of the original equation, we establish the existence of a generalized solution of the problem indicated.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 1, pp. 102–110, January, 2005. 相似文献
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非线性参数椭圆系统正解的存在性与多解性 总被引:4,自引:0,他引:4
本文讨论了一类非线性含参数椭圆系统正解的存在性与多解性,通过线性算子的谱半径,给出其正径向解存在与多解的条件,本质上改进和推广了文[1-3]的结果. 相似文献
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In this paper, we study the existence of solutions for the following impulsive fractional boundary-value problem: where \(\alpha \in (1/2, 1]\), \(0 = t_0< t_1< t_2< \cdots< t_n< t_{n +1} = T\), \(\lambda \) is a parameter and \(f :[0, T] \times {\mathbb {R}} \rightarrow {\mathbb {R}}\) and \(I_j : {\mathbb {R}} \rightarrow {\mathbb {R}}\), \(j = 1, \ldots , n\) are continuous functions and By using critical point theory and variational methods, we give some new criteria to guarantee that the impulsive problems have at least one solution and infinitely many solutions.
相似文献
$$\begin{aligned} {\left\{ \begin{array}{ll} - \frac{\mathrm{d}}{\mathrm{d}t} \Big (\frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t)) \Big ) = \lambda u (t) + f (t, u (t)), &{} t \ne t_j, \;\;\text {a.e.}\;\; t \in [0, T],\\ \Delta \Big (\frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j)) \Big ) = I_j (u (t_j)), &{} j = 1, 2, \ldots , n,\\ u (0) = u (T) = 0, \end{array}\right. } \end{aligned}$$
$$\begin{aligned}&\Delta \left( \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j)) \right) \\&\quad = \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j^+) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j^+) \\&\qquad -\, \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j^-) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j^-) ,\\&\frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j^+) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j^+)) \nonumber \\&\quad = \lim _{t \rightarrow t_j^+} \left( \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t))\right) ,\\&\frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t_j^-) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t_j^-)) \\&\quad = \lim _{t \rightarrow t_j^-} \left( \frac{1}{2} {}_0D_t^{\alpha - 1} ({}_0^c D_t^\alpha u (t) ) - \frac{1}{2} {}_tD_T^{\alpha - 1} ({}_t^c D_T^\alpha u (t))\right) . \end{aligned}$$
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We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule. 相似文献
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Existence and Multiplicity of Periodic Solutions of the Second-Order Differential Equations with Jumping Nonlinearities 总被引:2,自引:0,他引:2
Zai Hong Wang 《数学学报(英文版)》2002,18(3):615-624
We provide sufficient conditions for the existence and multiplicity of periodic solutions for Duffing's equations with jumping
nonlinearities under resonance conditions.
Received March 1, 1999, Revised September 16, 1999, Accepted February 1, 2000 相似文献
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椭圆边值系统的正径向解的存在性与多解性 总被引:2,自引:0,他引:2
通过利用锥拉伸及锥压缩型的Krasnosel‘skii不动点定理,我们研究了一类椭圆边值系统的正径向解的存在性,非存在性与多解性。 相似文献
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In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian
and
are studied and some new multiplicity results of solutions for systems (1.λ) and (2.λ) are obtained. Moreover, by using the
KKM principle we give also two new existence results of solutions for systems (1.1) and (2.1).
This Work is supported in part by the National Natural Science Foundation of China (10561011). 相似文献
((1.λ)) |
((2.λ)) |
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在Orlicz—Sobolev空间中利用临界点理论考虑了非齐次拟线性椭圆方程{-div((︱▽u︱)▽u)=μ︱u︱q-2u+λ︱u︱p-2u在Ω中,u=0在Ω上无穷多解的存在性,其中Ω是R~N中边界光滑的有界区域,μ,λ∈R是两个参数. 相似文献
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In this paper we will be concerned with questions of existence and multiplicity of radial nonnegative solutions of the quasilinear elliptic equation We will use variational methods in order to prove the existence of multiple solutions in case f is a sign-changing nonlinearity. 相似文献
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In this paper, we use the ordinary differential equation theory of Banach spaces and minimax theory, and in particular, the
relative mountain pass lemma to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,
and get new multiple solutions and sign-changing solutions theorems, at last we get up to six nontrivial solutions.
Received April 21, 1998, Revised November 2, 1998, Accepted January 14, 1999 相似文献
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本文应用Banach空间常微分方程和极大极小理论,特别是相对山路引理研究了零点和无穷远点跳跃非线性条件下椭圆边值问题的变号解和多解,得到新的变号解和多解存在性定理,最后我们得到6个非平凡解的存在性. 相似文献
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本文应用Banach空间常微分方程和极大极小理论,特别是相对山路引理研究了零点和无穷远点跳跃非线性条件下椭圆边值问题的变号解和多解,得到新的变号解和多解存在性定理,最后我们得到6个非平凡解的存在性. 相似文献
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