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The Cauchy problem for tenth-order thin film equation I. Bifurcation of oscillatory fundamental solutions
Pablo Alvarez-Caudevilla, Jonathan D. Evans, Victor A. Galaktionov
Fundamental global similarity solutions of the tenth-order thin film equation u_{t} = \nabla \cdot(|u|^{n} \n \D^4 u) in R^N \times R_+, where n>0 are studied. The main approach co…
The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions
Pablo Alvarez-Caudevilla, Jonathan D. Evans, Victor A. Galaktionov
Fundamental global similarity solutions of the standard form u_\g(x,t)=t^{-\a_\g} f_\g(y), with the rescaled variable y= x/{t^{\b_\g}}, \b_\g= \frac {1-n \a_\g}{10}, where \a_\g>0…
Countable families of solutions of a limit stationary semilinear fourth-order Cahn--Hilliard equation I. Mountain pass and Lusternik--Schnirel'man patterns in R^N
Pablo Alvarez-Caudevilla, Jonathan D. Evans, Victor A. Galaktionov
Solutions of the stationary semilinear Cahn--Hilliard equation -Δ^2 u - u -Δ(|u|^{p-1}u)=0 in R^N, with p>1, which are exponentially decaying at infinity, are studied. Using the Mo…
Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrödinger equations
P. Álvarez-Caudevilla, E. Colorado, V. A. Galaktionov
We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schrödinger equations. Actually, using the classical Mountain Pass Theor…