Solvability of Abstract Semilinear Equations by a Global Diffeomorphism Theorem
Sign Up to like & getrecommendations! Published in 2017 at "Results in Mathematics"
DOI: 10.1007/s00025-018-0873-y
Abstract: In this work we develop a method towards unique solvability of abstract semilinear equations. We use a global diffeomorphism theorem for which we provide a simplified proof. Applications to second order partial differential equations are… read more here.
Keywords: diffeomorphism theorem; global diffeomorphism; abstract semilinear; solvability abstract ... See more keywords
To the theory of semilinear equations in the plane
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-019-04519-z
Abstract: In two dimensions, we present a new approach to the study of the semilinear equations of the form div[A(z)∇u] = f(u), the diffusion term of which is the divergence uniform elliptic operator with measurable matrix… read more here.
Keywords: semilinear equations; equations plane; theory semilinear;
Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities
Sign Up to like & getrecommendations! Published in 2019 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2019.05.017
Abstract: We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian manifolds. As a… read more here.
Keywords: equations position; overdetermined boundary; dependent nonlinearities; position dependent ... See more keywords