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Perturbed Schrödinger lattice systems with superlinear terms: Multiplicity of homoclinic solutions
Calculus of Variations and Partial Differential Equations, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guanwei Chen, Shiwang Ma
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Fast homoclinic solutions for some second order non-autonomous systems [PDF]
Journal of Mathematical Analysis and Applications, 2011 This paper is concerned with the existence of homoclinic solutions for the following second order non-autonomous system(FHS)q¨+cq˙+Uq(t,q)=0, where q∈Rn, c⩾0 is a constant and U(t,q)∈C1(R×Rn,R).
Ziheng Zhang
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Acta Mathematica Sinica, English Series, 2022
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Liu, Peng, Guo, Fei
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Peng, Guo, Fei
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Multiple Homoclinic Solutions for Second‐Order Perturbed Hamiltonian Systems
Studies in Applied Mathematics, 2013In this paper, we study the second‐order perturbed Hamiltonian systems urn:x-wiley:00222526:sapm12023:equation:sapm12023-math-0001where is a parameter, is positive definite for all but unnecessarily uniformly positive definite for , and W is either asymptotically quadratic or superquadratic in x as .
Ye, Yiwei, Tang, Chun-Lei
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Existence and multiplicity of homoclinic solutions for a class of damped vibration problems
Nonlinear Analysis: Theory, Methods & Applications, 2011The following damped vibration problems are considered: \[ -\ddot{u}(t)-B\dot{u}(t)+A(t)u(t)=\nabla F(t,u(t))\text{ a.e. }t\in\mathbb{R}, \] \[ u(t)\rightarrow 0\text{ and }\dot{u}(t)\rightarrow 0\text{ as }|t|\rightarrow\infty, \] where \(A\in C(\mathbb{R},\mathbb{R}^{N^2})\) is an \(N\times N\) symmetric matrix-valued function, \(B\) is an ...
Wu, Xian, Zhang, Wei
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Multiplicity of homoclinic solutions for singular second-order conservative systems
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1996We consider a class of second-order systems, withq(t) ∊ℝn, for which the potential energyV: ℝn\S→ℝ admits a (possibly unbounded) singular setS⊂ℝnand has a unique absolute maximum at 0 ∈ℝn. Under some conditions on S andV, we prove the existence of several solutions homoclinic to 0.
Bertotti, Maria Letizia, Jeanjean, Louis
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MULTIPLICITY OF HOMOCLINIC SOLUTIONS FOR FRACTIONAL DISCRETE LAPLACIAN EQUATIONS
Rocky Mountain Journal of MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Mathematical Methods in the Applied Sciences, 2016
In this paper, a nonperiodic discrete nonlinear equation with Jacobi operators is considered. By using the critical point theory, we establish some new sufficient conditions on the existence and multiplicity of homoclinic solutions. Recent results are generalized and significantly improved.
Chen, Peng, He, Xiaofei
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In this paper, a nonperiodic discrete nonlinear equation with Jacobi operators is considered. By using the critical point theory, we establish some new sufficient conditions on the existence and multiplicity of homoclinic solutions. Recent results are generalized and significantly improved.
Chen, Peng, He, Xiaofei
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Mathematical Methods in the Applied Sciences
ABSTRACTBy means of the Ekeland variational principle coupled with the mountain pass lemma, we study a class of nonlinear second‐order parametric partial difference equations involving ‐Laplacian. Taking into account both the cases of large and small , we establish criteria to ensure the existence of two nontrivial homoclinic solutions for ...
Yuhua Long, Sha Li
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ABSTRACTBy means of the Ekeland variational principle coupled with the mountain pass lemma, we study a class of nonlinear second‐order parametric partial difference equations involving ‐Laplacian. Taking into account both the cases of large and small , we establish criteria to ensure the existence of two nontrivial homoclinic solutions for ...
Yuhua Long, Sha Li
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Journal of Difference Equations and Applications, 2011
In the present paper, we deal with the existence and multiplicity of homoclinic solutions of the second-order self-adjoint discrete Hamiltonian system where and are neither autonomous nor periodic in n. Under the assumption that is indefinite sign and subquadratic as and p(n) and L(n) are N × N real symmetric positive definite matrices for all , we ...
X. H. Tang, Xiaoyan Lin
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In the present paper, we deal with the existence and multiplicity of homoclinic solutions of the second-order self-adjoint discrete Hamiltonian system where and are neither autonomous nor periodic in n. Under the assumption that is indefinite sign and subquadratic as and p(n) and L(n) are N × N real symmetric positive definite matrices for all , we ...
X. H. Tang, Xiaoyan Lin
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