Results 31 to 40 of about 19,228,694 (296)
The Soap Bubble Theorem and a $p$-Laplacian overdetermined problem [PDF]
, 2019 We consider the $p$-Laplacian equation $-\Delta_p u=1$ for ...
Colasuonno, Francesca, Ferrari, Fausto
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Resonance Problems for the p-Laplacian
Journal of Functional Analysis, 1999 Using variational arguments the authors prove the existence of a weak solution for the boundary value problem \[ \begin{cases} -\Delta_p u-\lambda|u|^{p-2}u+f(x,u)=0\quad&\text{in }\Omega,\\ u=0\quad&\text{on }\partial\Omega,\end{cases} \] where \(\Delta_p u=\)div\((|Du|^{p-2}Du)\), \(p>1\), \(\Omega\) is a bounded domain of \(\mathbb R^N\), \(\lambda ...
Stephen B. Robinson, Pavel Drábek
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Eigenvalues for systems of fractional $p$-Laplacians [PDF]
Rocky Mountain Journal of Mathematics, 2018 We study the eigenvalue problem for a system of fractional $p-$Laplacians, that is, $$ \begin{cases} (- _p)^r u = \dfrac p|u|^{ -2}u|v|^ &\text{in } ,\vspace{.1cm} (- _p)^s u = \dfrac p|u|^ |v|^{ -2}v &\text{in } , u=v=0 &\text{in } ^c=\R^N\setminus . \end{cases} $$ We show that there is a first (smallest) eigenvalue that
Pezzo, Leandro M. Del, Rossi, Julio D.
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On the Fučí k spectrum for the $p$-Laplacian
Differential and Integral Equations, 2001 The structure of the set \(\{(\alpha, \beta) \in \mathbb R^2\): the problem \(-\Delta_p u = \alpha (u^+)^{p-1} - \beta (u^-)^{p-1}\) in \(\Omega\), \(u=0\) on \(\partial\Omega\) has a nontrivial solution\} is studied. See also \textit{N. Dancer} and \textit{K. Perera} [J. Math. Anal. Appl. 254, 164-177 (2001; Zbl 0970.35056)].
MICHELETTI, ANNA MARIA, A. PISTOIA
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Advances in Nonlinear Analysis, 2019 This paper concerns the existence and multiplicity of solutions for the Schrődinger–Kirchhoff type problems involving the fractional p–Laplacian and critical exponent.
Mingqi Xiang +2 more
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Oscillatory Property of Solutions for p(t)-Laplacian Equations
Journal of Inequalities and Applications, 2007 We consider the oscillatory property of the following p(t)-Laplacian equations −(|u'|p(t)−2u')'=1/tθ(t)g(t,u), t>0. Since there is no Picone-type identity for p(t)- Laplacian equations, it is an unsolved problem that whether the Sturmian ...
Qihu Zhang
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, 2020 This paper aims to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operator. By using the technique of Riccati transformation and the theory of comparison with first-order delay equations, we will ...
O. Bazighifan, T. Abdeljawad
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Landesman-Lazer conditions at half-eigenvalues of the p-Laplacian [PDF]
, 2012 We study the existence of solutions of the Dirichlet problem {gather} -\phi_p(u')' -a_+ \phi_p(u^+) + a_- \phi_p(u^-) -\lambda \phi_p(u) = f(x,u), \quad x \in (0,1), \label{pb.eq} \tag{1} u(0)=u(1)=0,\label{pb_bc.eq} \tag{2} {gather} where $p>1$, $\phi_p(
Genoud, François, Rynne, Bryan P.
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The principal eigencurve for the $p$-Laplacian
Differential and Integral Equations, 1995 The authors study the principal eigencurve \(\mu= \mu(\lambda)\) of the 2 parameter nonlinear eigenvalue problem \[ -\text{div} (| \nabla u|^{p-2} \nabla u)+ a(x)| u|^{p-2} u-\lambda m(x)| u|^{p-2}u= \mu| u|^{p-2} u \text{ in } \Omega, \quad u=0 \text{ on } \partial\Omega.
Binding, P. A., Huang, Y. X.
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A strong comparison principle for the $p$-Laplacian [PDF]
Proceedings of the American Mathematical Society, 2007 We consider weak solutions of the differential inequality of p-Laplacian type - Δpu - f(u) ≤-Δpv - f(v) such that u p - 1.
ROSELLI, PAOLO, Sciunzi, B.
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