Displaying similar documents to “Bounded and L 2 -solutions of certain third order non-linear differential equation with a square integrable forcing term”

On the solvability of nonlinear elliptic equations in Sobolev spaces

Piotr Fijałkowski (1992)

Annales Polonici Mathematici

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We consider the existence of solutions of the system (*) P ( D ) u l = F ( x , ( ∂ α u ) ) , l = 1,...,k, x ∈ ℝ n ( u = ( u ¹ , . . . , u k ) ) in Sobolev spaces, where P is a positive elliptic polynomial and F is nonlinear.

Nonsymmetric solutions of a nonlinear boundary value problem

Sámuel Peres (2014)

Czechoslovak Mathematical Journal

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We study the existence and multiplicity of positive nonsymmetric and sign-changing nonantisymmetric solutions of a nonlinear second order ordinary differential equation with symmetric nonlinear boundary conditions, where both of the nonlinearities are of power type. The given problem has already been studied by other authors, but the number of its positive nonsymmetric and sign-changing nonantisymmetric solutions has been determined only under some technical conditions. It was a long-standing...

On the Hammerstein equation in the space of functions of bounded ϕ -variation in the plane

Luis Azócar, Hugo Leiva, Jesús Matute, Nelson Merentes (2013)

Archivum Mathematicum

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In this paper we study existence and uniqueness of solutions for the Hammerstein equation u ( x ) = v ( x ) + λ ∫ I a b K ( x , y ) f ( y , u ( y ) ) d y , x ∈ I a b : = [ a 1 , b 1 ] × [ a 2 , b 2 ] , in the space B V ϕ ℝ ( I a b ) of function of bounded total ϕ - variation in the sense of Riesz, where λ ∈ ℝ , K : I a b × I a b → ℝ and f : I a b × ℝ → ℝ are suitable functions.

On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions

Joachim Naumann, Jörg Wolf, Michael Wolff (1998)

Commentationes Mathematicae Universitatis Carolinae

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We prove the interior Hölder continuity of weak solutions to parabolic systems ∂ u j ∂ t - D α a j α ( x , t , u , ∇ u ) = 0 in Q ( j = 1 , ... , N ) ( Q = Ω × ( 0 , T ) , Ω ⊂ ℝ 2 ), where the coefficients a j α ( x , t , u , ξ ) are measurable in x , Hölder continuous in t and Lipschitz continuous in u and ξ .