A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations

DOI10.1016/j.jmaa.2010.09.017zbMath1207.47064OpenAlexW2049115908MaRDI QIDQ615902

Cheng-Bo Zhai, Douglas R. Anderson

Publication date: 7 January 2011

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.09.017

zbMATH Keywords

fixed pointnormal conepositive solutionoperator equationelastic beam equationLane-Emden-Fowler equation

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Equations involving nonlinear operators (general) (47J05) Applications of operator theory to differential and integral equations (47N20) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
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• Unnamed Item
• Two-parameter nonresonance condition for the existence of fourth-order boundary value problems
• On \(\alpha\)-convex operators
• Multiple fixed points of a sum operator and applications
• Positive solutions of the three-point boundary value problem for second order differential equations with an advanced argument
• Ground state solutions for the singular Lane-Emden-Fowler equation with sublinear convection term
• Lane-Emden-Fowler equations with convection and singular potential
• A fixed point theorem for convex and decreasing operators
• Existence and iteration of monotone positive solutions for an elastic beam equation with a corner
• Monotone positive solutions for a fourth order equation with nonlinear boundary conditions
• Existence and approximation of solutions of non-linear elliptic equations
• Positive solutions of fourth-order two point boundary value problems.
• Sublinear singular elliptic problems with two parameters.
• Three symmetric positive solutions for a second-order boundary value problem
• Three positive fixed points of nonlinear operators on ordered Banach spaces
• A multiplicity result for second order impulsive differential equations via the Leggett Williams fixed point theorem
• Positive solutions for eigenvalue problems of fourth-order elastic beam equations.
• The upper and lower solution method for some fourth-order boundary value problems
• Positive solutions of operator equations on ordered Banach spaces and applications
• Nonlinear triple-point problems with change of sign
• Common fixed points for maps on cone metric space
• Linear and quasilinear elliptic equations
• The asymptotic behaviour of the unique solution for the singular Lane-Emden-Fowler equation
• On a singular nonlinear dirichlet problem
• A degenerate diffusion equation with a nonlinear source term
• On a Singular Nonlinear Elliptic Boundary-Value Problem
• Fixed point theorems in ordered abstract spaces
• Hilbert’s projective metric and iterated nonlinear maps
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• On a dirichlet problem with a singular nonlinearity
• On a singular nonlinear semilinear elliptic problem
• The contraction principle for mappings on a metric space with a graph
• Equivalent Norms for Sobolev Spaces
• Positive solutions for singular nonlinear elliptic equations
• Stability of positive fixed points of nonlinear operators

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