Results 11 to 20 of about 158 (97)
Open Mathematics, 2022 In this article, we study a class of Kirchhoff-type equation driven by the variable s(x, ⋅)-order fractional p1(x, ⋅) & p2(x, ⋅)-Laplacian. With the help of three different critical point theories, we obtain the existence and multiplicity of solutions in
Bu Weichun, An Tianqing, Zuo Jiabin
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Open Mathematics, 2022 In this article, we study two classes of Kirchhoff-type equations as follows: −a+b∫R3∣∇u∣2dxΔu+V(x)u=(Iα∗∣u∣p)∣u∣p−2u+f(u),inR3,u∈H1(R3),\left\{\begin{array}{l}-\left(a+b\underset{{{\mathbb{R}}}^{3}}{\overset{}{\int }}| \nabla u{| }^{2}{\rm{d}}x\right ...
Zhou Li, Zhu Chuanxi
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Bäcklund transformations for several cases of a type of generalized KdV equation
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 63, Page 3369-3377, 2004., 2004 An alternate generalized Korteweg‐de Vries system is studied here. A procedure for generating solutions is given. A theorem is presented, which is subsequently applied to this equation to obtain a type of Bäcklund transformation for several specific cases of the power of the derivative term appearing in the equation. In the process, several interesting,
Paul Bracken
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Variational approach to dynamics of bright solitons in lossy optical fibers
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 49, Page 3143-3148, 2003., 2003 A variational analysis of dynamics of soliton solution of coupled nonlinear Schrödinger equations with oscillating terms is made, considering a birefringent fiber with a third‐order nonlinearity in the anomalous dispersion frequency region. This theoretical model predicts optical soliton oscillations in lossy fibers.
M. F. Mahmood, S. Brooks
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Eigenfrequencies of generally restrained beams
Journal of Applied Mathematics, Volume 2003, Issue 10, Page 503-516, 2003., 2003 We deal with the exact determination of eigenfrequencies of a beam with intermediate elastic constraints and generally restrained ends. It is the purpose of this paper to use the calculus of variations to obtain the equations of motion and the natural boundary conditions, and particularly those at the intermediate constraints.
Ricardo Oscar Grossi +1 more
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Sign-Changing Solutions for a Class of Zero Mass Nonlocal Schrödinger Equations
Advanced Nonlinear Studies, 2019 We consider the following class of fractional Schrödinger equations:
Ambrosio Vincenzo +3 more
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Perturbations near resonance for the p‐Laplacian in ℝN
Abstract and Applied Analysis, Volume 7, Issue 6, Page 323-334, 2002., 2002 We study a multiplicity result for the perturbed p‐Laplacian equation −Δpu − λg(x)|u|p−2u = f(x, u) + h(x) in ℝN, where 1 < p < N and λ is near λ 1, the principal eigenvalue of the weighted eigenvalue problem −Δpu = λg(x)|u|p−2u in ℝN. Depending on which side λ is from λ 1, we prove the existence of one or three solutions.
To Fu Ma, Maurício Luciano Pelicer
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Abstract and Applied Analysis, Volume 7, Issue 10, Page 547-561, 2002., 2002 We study the location of the peaks of solution for the critical growth problem −ε 2Δu+u=f(u)+u 2*−1, u > 0 in Ω, u = 0 on ∂Ω, where Ω is a bounded domain; 2* = 2N/(N − 2), N ≥ 3, is the critical Sobolev exponent and f has a behavior like up, 1 < p < 2* − 1.
Marco A. S. Souto
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Multiple solutions for a problem with resonance involving the p‐Laplacian
Abstract and Applied Analysis, Volume 3, Issue 1-2, Page 191-201, 1998., 1998 In this paper we will investigate the existence of multiple solutions for the problem where Δpu = div(|∇u|p−2∇u) is the p‐Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N ≥ 1 and 1 < p < ∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least ...
C. O. Alves +2 more
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Existence and multiplicity of solutions for a class of p-Kirchhoff-type equation RN
Open Mathematics, 2023 This article shows the existence and multiplicity of solutions for the following pp-Kirchhoff-type equation: a+b∫RN(∣∇u∣p+V(x)∣u∣p)dx(−△pu+V(x)∣u∣p−2u)=λg(x)∣u∣r−2u−h(x)∣u∣q−2u,inRN.\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{N}}\left({| \nabla u| }^{
Chen Lijuan +2 more
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