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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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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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A fractional Kirchhoff problem involving a singular term and a critical nonlinearity [PDF]
, 2017 In this paper we consider the following critical nonlocal problem $$ \left\{\begin{array}{ll} M\left(\displaystyle\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dxdy\right)(-\Delta)^s u = \displaystyle\frac{\lambda}{u^\gamma}+u^{2^*_s-1}&\quad ...
Fiscella, Alessio
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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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Existence of high energy solutions for Kirchhoff-type equations [PDF]
Proceedings of the 2nd International Conference On Systems Engineering and Modeling, 2013 In this paper, by applying the fountain theorems, we study the existence of infinitely many high energy solutions for the nonlinear kirchhoff nonlocal equations under the Ambrosetti-Rabinowitz type growth conditions or no Ambrosetti-Rabinowitz type growth conditions, infinitely many high energy solutions are obtained.
Chun Han Liu, Jian Guo Wang
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Global well-posedness of the Kirchhoff equation and Kirchhoff systems [PDF]
, 2014 This article is devoted to review the known results on global well-posedness for the Cauchy problem to the Kirchhoff equation and Kirchhoff systems with small data.
E Callegari +22 more
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Liouville theorems for Kirchhoff-type parabolic equations and system on the Heisenberg group
Open Mathematics, 2023 In this article, the Liouville theorems for the Kirchhoff-type parabolic equations on the Heisenberg group were established. The main technique for proving the result relies on the method of test functions.
Shi Wei
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Global well-posedness of Kirchhoff systems [PDF]
, 2012 The aim of this paper is to establish the $H^1$ global well-posedness for Kirchhoff systems. The new approach to the construction of solutions is based on the asymptotic integrations for strictly hyperbolic systems with time-dependent coefficients. These
Bernstein +24 more
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Concentration phenomena for a fractional Schrödinger‐Kirchhoff type equation
Mathematical Methods in the Applied Sciences, 2017 In this paper, we deal with the multiplicity and concentration of positive solutions for the following fractional Schrödinger‐Kirchhoff type equation urn:x-wiley:mma:media:mma4633:mma4633-math-0001 where ε>0 is a small parameter, is the fractional Laplacian, M is a Kirchhoff function, V is a continuous positive potential, and f is a superlinear ...
Vincenzo Ambrosio, Teresa Isernia
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Multiplicity result for non-homogeneous fractional Schrodinger--Kirchhoff-type equations in ℝn
Advances in Nonlinear Analysis, 2018 In this paper we consider the existence of multiple solutions for the non-homogeneous fractional p-Laplacian equations of Schrödinger–Kirchhoff ...
Torres Ledesma César E.
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