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New iterative methods for nonlinear equations in R
International Journal of Mathematics in Operational Research, 2016A parameter based on two-step iterative method combining two known third order methods is proposed for solving nonlinear equations in R. The convergence analysis of the method is established to show its fourth order of convergence. In order to enhance the order of convergence from four to seven, its three-step extension is also developed.
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Negative Eigenvalues for a Nonlinear Differential Equation on $\mathbb{R}$
SIAM Journal on Mathematical Analysis, 1993The nonlinear Dirichlet problem \(-u''-q(t)| u |^{\sigma_ 1}u+r(t) | u |^{\sigma_ 2}u=\lambda u\), \(\lim_{t \to \pm \infty}u(t)=0\) is considered. Conditions are given which imply the existence of a negative eigenvalue and a positive classical solution decaying exponentially at \(\pm \infty\). This generalizes results by Beresticky-Lions for constant \
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A positive solution for a nonlinear Schroedinger equation on R^N
Indiana University Mathematics Journal, 2005We prove the existence of a positive solution for a class of equations of the form -Δu + V(x)u = f(u), u ∈ H 1 (R N ). On the nonlinearity f, only conditions around 0 and at oo are required.
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