Maximum and comparison principles for operators involving the \(p\)-Laplacian

DOI10.1006/jmaa.1997.5732zbMath0897.35015OpenAlexW2068396973MaRDI QIDQ1380309

José C. Sabina De Lis, Jorge García-Melián

Publication date: 4 March 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5732

zbMATH Keywords

first eigenvaluestrong positivity

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Maximum principles in context of PDEs (35B50) Degenerate elliptic equations (35J70)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Strong positivity in \(C(\bar\Omega)\) for elliptic systems
• A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
• A theorem on elliptic differential inequalities with an application to gradient bounds
• Regularity for a more general class of quasilinear equations
• The maximum principle for cooperative weakly coupled elliptic systems and some applications
• On maximum principles and existence of positive solutions for some cooperative elliptic systems
• The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems
• A strong maximum principle for some quasilinear elliptic equations
• Local behavior of solutions of quasi-linear equations
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• On The Dirichletproblem for Quasilinear Equations
• Remarks on sublinear elliptic equations
• Remarks on uniqueness results of the first eigenvalue of the p-Laplacian
• Generalization of Fredholm alternative for nonlinear differential operators
• Boundary regularity for solutions of degenerate elliptic equations
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• The Minimum Principle for Elliptic Systems
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• On the spectrum of general second order operators

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