Fractional Kirchhoff-Type and Method of Sub-supersolutions
Differential Equations and Dynamical Systems, 2023 In the present paper, we are interested in investigating the existence of positive solutions of a new class of fractional Kirchhoff via the sub and supersolutions technique. For this, we first need to investigate two results through lemmas.
JOSÉ Vanterler Sousa +1 more
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Existence results for quasilinear problems via ordered sub and supersolutions [PDF]
Annales De La Faculté Des Sciences De Toulouse, 1997 The author proves the existence of maximal and minimal solutions between an ordered pair of weak sub- and supersolutions of the quasilinear problem \[ -\text{div} \bigl( | \nabla u|^{p-2} \nabla u\bigr) =f(x,u, \nabla u) \quad \text{in }\Omega \] with \(u=0\) on \(\partial \Omega\).
exaly +3 more sources
Sub- and supersolutions for semilinear elliptic equations on all of $\mathbb{R}^n$
Differential and Integral Equations, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
K J Brown
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Revisiting the method of sub- and supersolutions for nonlinear elliptic problems
Electronic Journal of Differential Equations, 2007 We discuss some of the historical highlights of the theory of sub- supersolutions for boundary value problems for nonlinear elliptic equations and variational inequalities.
Klaus Schmitt
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A remark on the existence of large solutions via sub and supersolutions
Electronic Journal of Differential Equations, 2003 We study the boundary blow-up elliptic problem $Delta u=a(x) f(u)$ in a smooth bounded domain $Omegasubset mathbb{R}^N$, with $u|_{partialOmega}=+infty$. Under suitable growth assumptions on $a$ near $partialOmega$ and on $f$ both at zero and at infinity,
Jorge Garcia-Melian
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An existence result for a class of Kirchhoff type systems via sub and supersolutions method
Applied Mathematics Letters, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nguyen Thanh Chung
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Sub-supersolution theorems for quasilinear elliptic problems: A variational approach
Electronic Journal of Differential Equations, 2004 This paper presents a variational approach to obtain sub - supersolution theorems for a certain type of boundary value problem for a class of quasilinear elliptic partial differential equations.
Vy Khoi Le, Klaus Schmitt
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Singular quasilinear convective systems involving variable exponents [PDF]
Opuscula Mathematica, 2023 The paper deals with the existence of solutions for quasilinear elliptic systems involving singular and convection terms with variable exponents. The approach combines the sub-supersolutions method and Schauder's fixed point theorem.
Abdelkrim Moussaoui +2 more
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A sub-supersolution approach for a quasilinear Kirchhoff equation [PDF]
Journal of Mathematical Physics, 2015 In this paper, we establish an existence result for a quasilinear Kirchhoff equation, via a sub- and supersolution approach, by using the Minty-Browder’s Theorem for pseudomonotone operators theory.
Alves, Claudianor O. +1 more
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The sub-supersolution method for weak solutions [PDF]
Proceedings of the American Mathematical Society, 2008 Summary: We extend the method of sub- and supersolutions in order to prove existence of \(L^1\)-solutions of the equation \(-\Delta u = f(x,u)\) in \(\Omega\), where \(f\) is a Carathéodory function. The proof is based on the Schauder's fixed point theorem.
Montenegro, Marcelo, Ponce, Augusto C.
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