Titlebook: Entire Solutions of Semilinear Elliptic Equations; I. Kuzin,S. Pohozaev Book 1997 Bikhäuser Verlag 1997 Finite.Identity.Invariant.equation

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Verantwortung und Wissenschaft,We saw in §12 that noncoercive problems .can be studied with the help of theorems on a conditional minimum if . is homogeneous. However such . are rare.

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https://doi.org/10.1007/978-3-0348-7962-0In this chapter, we consider the equation . where we denote . = |x|.

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Industrial Marketing GenerationsThe Laplace operator possesses a remarkable feature of monotonicity permitting us to study the solvability of elliptic problems. The statement is given in Theorem 25.1.

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Classical Variational Method,In this chapter and throughout the book, we shall consider boundary problems of the form. Functions . : ℝ. x ℝ → ℝ are supposed to satisfy a so-called Carathéodory condition, i.e., to be continuous with respect to . for almost all x ∈ ℝ. and measurable in x for all . ∈ ℝ.

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Variational Methods for Eigenvalue Problems,Up to now we have studied problems of a coercive type. Investigation of noncoercive problems requires other methods. One of the ways is the reduction of an original elliptic problem to a new one with a free parameter (eigenvalue) and the investigation of this new problem, for example, by the method of a conditional extremum.

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Radial Solutions: The ODE Method,In this chapter, we consider the equation . where we denote . = |x|.