On symmetric positive homoclinic solutions of semilinear \(p\)-Laplacian differential equations

DOI10.1186/1687-2770-2012-121zbMath1281.34032OpenAlexW2131707838WikidataQ59272715 ScholiaQ59272715MaRDI QIDQ384444

Stepan Agop Tersian

Publication date: 27 November 2013

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-2770-2012-121

zbMATH Keywords

weak solutionmountain pass theoremPalais-Smale conditionhomoclinic solution\(p\)-Laplacian ordinary differential equations

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

Related Items (8)

Multiple homoclinic solutions for \(p\)-Laplacian Hamiltonian systems with concave-convex nonlinearities ⋮ Homoclinic solutions for \(p\)-Laplacian Hamiltonian systems with combined nonlinearities ⋮ Existence of positive homoclinic solutions for damped differential equations ⋮ Homoclinic solutions for Hamiltonian systems of \(p\)-Laplacian-like type ⋮ Existence of two periodic solutions to general anisotropic Euler-Lagrange equations ⋮ Mountain pass type periodic solutions for Euler-Lagrange equations in anisotropic Orlicz-Sobolev space ⋮ Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters ⋮ Unique iterative positive solutions for a singular \(p\)-Laplacian fractional differential equation system with infinite-point boundary conditions

Cites Work

• Homoclinic solutions for ordinary \(p\)-Laplacian systems with a coercive potential
• Symmetry and related properties via the maximum principle
• The Fredholm alternative at the first eigenvalue for the one dimensional \(p\)-Laplacian
• Positive homoclinic solutions for a class of second order differential equations
• Dual variational methods in critical point theory and applications
• Some existence results on periodic solutions of ordinary \(p\)-Laplacian systems
• Biomathematical model of aneurysm of the circle of Willis. I: The Duffing equation and some approximate solutions
• Biomathematical model of aneurysm of the circle of Willis: a qualitative analysis of the differential equation of Austin
• A note on periodic solutions of some nonautonomous differential equations
• Homoclinic orbits for a class of Hamiltonian systems

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