Abstract
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given by Soltanov in Nonlinear Anal. 72:164–175, 2010 for studying the nonlinear continuous operator. Moreover we reduce certain general results for the continuous operators acting on Banach spaces, and investigate their image. Here we also consider the existence of a fixed-point of the continuous operators under various conditions.
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- 1.
In particular, the mapping g can be a linear bounded operator as g≡L:X⟶Y ∗ that satisfy the conditions of (ii).
- 2.
In particular, g≡J:X⟶X ∗, i.e. g be a duality mapping.
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Soltanov, K.N. (2015). Nonlinear Operators, Fixed-Point Theorems, Nonlinear Equations. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_41
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DOI: https://doi.org/10.1007/978-3-319-12577-0_41
Publisher Name: Birkhäuser, Cham
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