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Multiple solutions for a fractional p-Laplacian equation with sign-changing potential
Electronic Journal of Differential Equations, 2016 We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the fractional p-Laplace equation $$\displaylines{ (-\Delta)_p^s u + V(x) |u|^{p-2}u = f(x, u) \quad \text{in } \mathbb{R}^N, }$$ where $s\in (0,1)
Vincenzo Ambrosio
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper we consider the Dirichlet problem for quasi-linear second-order elliptic equation with the $m(x)$-Laplacian and the strong nonlinearity on the right side in an unbounded cone-like domain.
Mikhail Borsuk, Damian Wiśniewski
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Positive radial solutions of p-Laplace equations on exterior domains
AIMS Mathematics, 2021 This paper deals with the existence of positive radial solutions of the $ p $-Laplace equation $ \left\{\begin{array}{ll} -\Delta_p\,u= K(|x|)\,f(u)\,,\quad x\in\Omega\,,\qquad\qquad\\[6pt] \frac{\partial u}{\partial n}=0\,,\qquad x\in\partial ...
Yongxiang Li, Mei Wei
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Local Polya fluctuations of Riesz gravitational fields and the Cauchy problem
Karpatsʹkì Matematičnì Publìkacìï, 2023 We consider a pseudodifferential equation of parabolic type with a fractional power of the Laplace operator of order $\alpha\in(0;1)$ acting with respect to the spatial variable.
V.A. Litovchenko
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Existence of weak solutions for quasilinear Schrödinger equations with a parameter
Electronic Journal of Qualitative Theory of Differential Equations, 2020 In this paper, we study the following quasilinear Schrödinger equation of the form \begin{equation*} -\Delta_{p}u+V(x)|u|^{p-2}u-\left[\Delta_{p}(1+u^{2})^{\alpha/2}\right]\frac{\alpha u}{2(1+u^{2})^{(2-\alpha)/2}}=k(u),\qquad x\in \mathbb{R}^{N}, \end ...
Yunfeng Wei +3 more
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The Parabolic Infinite-Laplace Equation in Carnot groups [PDF]
, 2014 By employing a Carnot parabolic maximum principle, we show existence-uniqueness of viscosity solutions to a class of equations modeled on the parabolic infinite Laplace equation in Carnot groups.
Bieske, Thomas, Martin, Erin
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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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Topological computation of some Stokes phenomena on the affine line [PDF]
, 2019 Let $\mathcal M$ be a holonomic algebraic $\mathcal D$-module on the affine line, regular everywhere including at infinity. Malgrange gave a complete description of the Fourier-Laplace transform $\widehat{\mathcal M}$, including its Stokes multipliers at
D'Agnolo, Andrea +3 more
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The Numerical Calculation of Traveling Wave Solutions of Nonlinear Parabolic Equations [PDF]
, 1986 Traveling wave solutions have been studied for a variety of nonlinear parabolic problems. In the initial value approach to such problems the initial data at infinity determines the wave that propagates.
Hagstrom, Thomas, Keller, H. B.
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The p-Laplace equation in domains with multiple crack section via pencil operators [PDF]
, 2014 The p-Laplace equation $$ \n \cdot (|\n u|^n \n u)=0 \whereA n>0, $$ in a bounded domain $\O \subset \re^2$, with inhomogeneous Dirichlet conditions on the smooth boundary $\p \O$ is considered.
Alvarez-Caudevilla, Pablo +1 more
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