Homoclinic Solution to Zero of a Non-autonomous, Nonlinear, Second Order Differential Equation with Quadratic Growth on the Derivative

Homoclinic Solution to Zero of a Non-autonomous, Nonlinear, Second Order Differential Equation with Quadratic Growth on the Derivative

This work aims to obtain a positive, smooth, even, and homoclinic to zero (i.e zero at infinity) solution to a non-autonomous, second-order, nonlinear differential equation involving quadratic growth on the derivative. We apply Galerkin's method combined with Strauss' approximation on the...

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Hauptverfasser: Junior, Pablo dos Santos Corrêa, Faria, Luiz Fernando de Oliveira
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Mathematics - Analysis of PDEs
Mathematics - Classical Analysis and ODEs
Mathematics - Mathematical Physics
Physics - Mathematical Physics
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description This work aims to obtain a positive, smooth, even, and homoclinic to zero (i.e zero at infinity) solution to a non-autonomous, second-order, nonlinear differential equation involving quadratic growth on the derivative. We apply Galerkin's method combined with Strauss' approximation on the term involving the first derivative to obtain weak solutions. We also study the regularity of the solutions and the dependence on their existence with a parameter
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subjects Mathematics - Analysis of PDEs
Mathematics - Classical Analysis and ODEs
Mathematics - Mathematical Physics
Physics - Mathematical Physics
title Homoclinic Solution to Zero of a Non-autonomous, Nonlinear, Second Order Differential Equation with Quadratic Growth on the Derivative
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