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Oscillation criteria for the Schrodinger PDE 495511
Bifurcation from Sshaped solution curves in a class of SturmLiouville problems
The CahnHilliard equation for deformable elastic
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a.e. in Q absolutely continuous Anal approximation assume assumptions asymptotic Banach space bifurcation boundary conditions bounded Cahn-Hilliard equation Co-semigroup coefficients compact consider continuous function convergence convex Corollary deduce defined denote depending differential equations domain dynamics eigenvalue elliptic equation 1.1 evolution equations exponential growth finite Fourier free energy density Gronwall's lemma Helmholtz free energy Hence Hilbert space holds implies inequality integrated semigroup Lemma Lipschitz Lipschitz continuous Malthusian parameter Math method mild solution modulus of continuity Moreover nonlinear nonlocal nonnegative norm numerical obtain optimal parabolic perturbation phase interface positive constant positive solution problem 1.2 proof of Theorem prove regular Remark respectively satisfying Sciences and Applications Section singular Sobolev spaces solutions of 1.1 spectral subset supersolution term Test Problem Theorem 2.1 theory Thieme uniformly unique solution value problem viscosity solutions weak solution weakly zero