Results 21 to 30 of about 43,034 (224)
Three nontrivial solutions for nonlinear fractional Laplacian equations
Advances in Nonlinear Analysis, 2018 We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three non-zero solutions.
Düzgün Fatma Gamze +1 more
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On singular solutions for second order delayed differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2012 Asymptotic properties and estimate of singular solutions (either defined on a finite interval only or trivial in a neighbouhood of infinity) of the second order delay differential equation with p-Laplacian are investigated.
Miroslav Bartusek
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Local versus nonlocal elliptic equations: short-long range field interactions
Advances in Nonlinear Analysis, 2020 In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian.
Cassani Daniele +2 more
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Fractional p&q-Laplacian problems with potentials vanishing at infinity [PDF]
Opuscula Mathematica, 2020 In this paper we prove the existence of a positive and a negative ground state weak solution for the following class of fractional \(p\&q\)-Laplacian problems \[\begin{aligned} (-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u + V(x) (|u|^{p-2}u + |u|^{q-2}u)= K(
Teresa Isernia
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An Eigenvalue problem for the Infinity-Laplacian
Electronic Journal of Differential Equations, 2012 36 pages Accepted to EJDE.
Tilak Bhattacharya, Leonardo Marazzi
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Optimal regularity for the pseudo infinity Laplacian [PDF]
ESAIM: Control, Optimisation and Calculus of Variations, 2007 The paper deals with optimal regularity for the viscosity solutions of the pseudo infinity Laplace equation given by \[ \widetilde\Delta_\infty = \sum_{i\in I(\nabla u)} u_{x_ix_i}| u_{x_i}| ^2, \] where the summation is taken over the indices in \(I(\nabla u)=\{i: | u_{x_i}| =\max_j | u_{x_j}| \}.\) Local Lipschitz continuity is proved for the ...
Rossi, J.D., Saez, M.
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Multiple Solutions for a Class of p(x)-Laplacian Systems
Journal of Inequalities and Applications, 2009 We study the multiplicity of solutions for a class of Hamiltonian systems with the p(x)-Laplacian. Under suitable assumptions, we obtain a sequence of solutions associated with a sequence of positive energies going toward infinity.
Yongqiang Fu, Xia Zhang
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Infinity Laplacian equation with strong absorptions
Journal of Functional Analysis, 2016 We study regularity properties of solutions to reaction-diffusion equations ruled by the infinity laplacian operator. We focus our analysis in models presenting plateaus, i.e. regions where a non-negative solution vanishes identically. We obtain sharp geometric regularity estimates for solutions along the boundary of plateaus sets.
Damião J. Araújo +2 more
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Adjoint Methods for the Infinity Laplacian Partial Differential Equation [PDF]
Archive for Rational Mechanics and Analysis, 2011 The authors consider the boundary value problem \[ \begin{cases} -\Delta_\infty u=0 \;\text{ in } U \cr u=g \;\text{ on } \partial U \end{cases} \] where \(\Delta_\infty u= u_{x_i}u_{x_j}u_{x_ix_j}\) and \(g\) is Lipschitz continuous. To study fine properties of certain smooth approximations \({u^\varepsilon}\) to a viscosity solution \(u\) of the ...
Evans, Lawrence C., Smart, Charles K.
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Nonlocal Tug‐of‐War and the Infinity Fractional Laplacian [PDF]
Communications on Pure and Applied Mathematics, 2011 AbstractMotivated by the “tug‐of‐war” game studied by Peres et al. in 2009, we consider a nonlocal version of the game that goes as follows: at every step two players pick, respectively, a direction and then, instead of flipping a coin in order to decide which direction to choose and then moving a fixed amount ϵ > 0 (as is done in the ...
Bjorland, Clayton +2 more
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