An inverse problem related to a half-linear eigenvalue problem
Boundary Value Problems, 2014 We study an inverse problem on the half-linear Dirichlet eigenvalue problem −(|y′(x)|p−2y′(x))′=(p−1)λr(x)|y(x)|p−2y(x), where p>1 with p≠2 and r is a positive function defined on [0,1].
Wei-Chuan Wang, Yan-Hsiou Cheng
semanticscholar +2 more sources
On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets [PDF]
, 2019 Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$.
Berg, M. van den +3 more
core +2 more sources
The "hot spots" conjecture on the Vicsek set
Demonstratio Mathematica, 2019 We prove the “hot spots” conjecture on the Vicsek set. Specifically, we will show that every eigenfunction of the second smallest eigenvalue of the Neumann Laplacian on the Vicsek set attains its maximum and minimum on the boundary.
Ionescu Marius, Savage Thomas L.
doaj +1 more source
Worst-case shape optimization for the Dirichlet energy [PDF]
, 2016 We consider the optimization problem for a shape cost functional $F(\Omega,f)$ which depends on a domain $\Omega$ varying in a suitable admissible class and on a "right-hand side" $f$. More precisely, the cost functional $F$ is given by an integral which
Bellido, José Carlos +2 more
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Multiplicity of solutions to discrete inclusions with the p(k)-Laplace type equations
Nonautonomous Dynamical Systems, 2018 In this article, we prove the existence and multiplicity of solutions to discrete inclusions with the p(k)-Laplace type equations. We are interested in the existence of three solutions with the aid of linking arguments and using a three critical points ...
Ouaro Stanislas, Zoungrana Malick
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MULTIPLICITY OF SOLUTIONS TO DISCRETE INCLUSIONS WITH THE p(k)-LAPLACE KIRCHHOFF TYPE EQUATIONS
, 2018 . This paper is concerned with the existence and multiplicity of solutions to discrete inclusions with an anisotropic discrete boundary value problem of p(k)-Laplace Kirchhoff type. Our technical approach is based on variational methods. 2010 Mathematics
S. Ouaro, Malick Zoungrana
semanticscholar +1 more source
Semi-classical States for Non-self-adjoint Schrodinger Operators
, 1998 We prove that the spectrum of certain non-self-adjoint Schrodinger operators is unstable in the semi-classical limit. Similar results hold for a fixed operator in the high energy limit.
Davies, E B
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Minimization of $\lambda_2(\Omega)$ with a perimeter constraint [PDF]
, 2009 We study the problem of minimizing the second Dirichlet eigenvalue for the Laplacian operator among sets of given perimeter. In two dimensions, we prove that the optimum exists, is convex, regular, and its boundary contains exactly two points where the ...
Bucur, Dorin +2 more
core +4 more sources
Weak homoclinic solutions to discrete nonlinear problems of Kirchhoff type with variable exponents
, 2017 In this paper, we prove the existence of weak homoclinic solutions for discrete nonlinear problems of Kirchhoff type. The proof of the main result is based on a minimization method. As extension, we prove the existence result of weak homoclinic solutions
A. Guiro, I. Ibrango, S. Ouaro
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Weak homoclinic solutions of anisotropic difference equation with variable exponents
Advances in Differential Equations, 2012 In this paper, we prove the existence of homoclinic solutions for a family of anisotropic difference equations. The proof of the main result is based on a minimization method and a discrete Hölder type inequality. MSC:47A75, 35B38, 35P30, 34L05, 34L30.
A. Guiro, B. Kone, S. Ouaro
semanticscholar +1 more source