Results 11 to 20 of about 1,647 (209)
Multiple Sign-Changing Solutions for Kirchhoff-Type Equations [PDF]
Discrete Dynamics in Nature and Society, 2015 We study the following Kirchhoff-type equations -a+b∫Ω∇u2dxΔu+Vxu=fx,u, in Ω, u=0, in ∂Ω, where Ω is a bounded smooth domain of RN (N=1,2,3), a>0, b≥0, f∈C(Ω¯×R,R), and V∈C(Ω¯,R).
Xingping Li, Xiumei He
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Existence of solutions for Kirchhoff type equations
Electronic Journal of Differential Equations, 2015 In this article, we prove the existence of solutions for Kirchhoff type equations with Dirichlet boundary-value condition. We use the Mountain Pass Theorem in critical point theory, without the (PS) condition.
Qi-Lin Xie, Xing-Ping Wu, Chun-Lei Tang
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Ground State Solutions for Kirchhoff Type Quasilinear Equations
Advanced Nonlinear Studies, 2019 In this paper, we are concerned with quasilinear equations of Kirchhoff type, and prove the existence of ground state signed solutions and sign-changing solutions by using the Nehari method.
Liu Xiangqing, Zhao Junfang
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Eigenvalue problems for p(x)-Kirchhoff type equations
Electronic Journal of Differential Equations, 2013 In this article, we study the nonlocal $p(x)$-Laplacian problem $$\displaylines{ -M\Big(\int_{\Omega}\frac{1}{p(x)}|\nabla u|^{p(x)}dx\Big) \hbox{div}(|\nabla u|^{p(x)-2}\nabla u)= \lambda|u|^{q(x)-2}u \quad \text{ in } \Omega,\cr u=0 \quad \text{on
Ghasem A. Afrouzi, Maryam Mirzapour
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On the Kirchhoff type equations in $\mathbb{R}^{N}$
Advances in Differential Equations, 2022 Consider a nonlinear Kirchhoff type equation as follows \begin{equation*} \left\{ \begin{array}{ll} -\left( a\int_{\mathbb{R}^{N}}|\nabla u|^{2}dx+b\right) Δu+u=f(x)\left\vert u\right\vert ^{p-2}u & \text{ in }\mathbb{R}^{N}, \\ u\in H^{1}(\mathbb{R}^{N}), & \end{array}% \right.
Sun, Juntao, Wu, Tsung-Fang
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n-Kirchhoff type equations with exponential nonlinearities [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2015 Results from earlier version are improved. RACSAM - Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A.
Goyal, Sarika +2 more
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Existence and Concentration Results for the General Kirchhoff-Type Equations
The Journal of Geometric Analysis, 2023 We consider the following singularly perturbed Kirchhoff type equations $$-\varepsilon^2 M\left(\varepsilon^{2-N}\int_{\R^N}|\nabla u|^2 dx\right)Δu +V(x)u=|u|^{p-2}u~\hbox{in}~\R^N, u\in H^1(\R^N),N\geq 1,$$ where $M\in C([0,\infty))$ and $V\in C(\R^N)$ are given functions.
Yinbin Deng, Wei Shuai, Xuexiu Zhong
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SOLUTIONS FOR THE KIRCHHOFF TYPE EQUATIONS WITH FRACTIONAL LAPLACIAN
Journal of Applied Analysis & Computation, 2020 Summary: Due to the singularity and nonlocality of the fractional Laplacian, the classical tools such as Sturm comparison, Wronskians, Picard-Lindelöf iteration, and shooting arguments (which are all purely local concepts) are not{ applicable} when analyzing solutions in the setting of the nonlocal operator \((-\Delta)^s\).
Jia, Yanping, Gao, Ying, Zhang, Guang
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An Existence Result for Fractional Kirchhoff-Type Equations
Zeitschrift für Analysis und ihre Anwendungen, 2016 The aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchhoff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods.
Bisci, G., TULONE, Francesco
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Existence of nontrivial solutions for p-Kirchhoff type equations [PDF]
Boundary Value Problems, 2013 The authors make use of the linking theorem and the mountain pass theorem to show the existence of nontrivial solutions for the nonlocal elliptic \(p\)-Kirchhoff equations without assuming Ambrosetti-Rabinowitz type growth conditions. At least one nontrivial weak solution, in the space \(W_0^{1,p}(\Omega),\) is obtained. The weak solutions of the above
Liu, Chunhan +2 more
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