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The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued spaces are given. Sharp estimates for resolvent, discreetness of spectrum, and completeness of root elements of the corresponding differential operators are obtained. In the last section, some applications of the main results are given.

The paper discusses the existence of positive solutions, dead core solutions, and pseudo dead core solutions of the singular problem , , . Here is a positive parameter, , , , may be singular at and is singular at .

This study focuses on nonlocal boundary value problems for elliptic ordinary and partial differential-operator equations of arbitrary order, defined in Banach-valued function spaces. The region considered here has a varying bound and depends on a certain parameter. Several conditions are obtained that guarantee the maximal regularity and Fredholmness, estimates for the resolvent, and the completeness of the root elements of differential operators generated by the corresponding boundary value problems in Banach-valued weighted spaces. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations and systems of anisotropic partial differential equations on cylindrical domain to obtain the algebraic conditions that guarantee the same properties.

In this paper, we present the abstract results for the existence and uniqueness of the solution of nonlinear elliptic systems, parabolic systems and integro-differential systems involving the generalized $(p,q)$-Laplacian operator. Our method makes use of the characteristics of the ranges of linear and nonlinear maximal monotone operators and the subdifferential of a proper, convex, and lower-semi-continuous functional, and we employ some new techniques in the construction of the operators and in proving the properties of the newly defined operators. The systems discussed in this paper and the method used extend and complement some of the previous work. [ABSTRACT FROM AUTHOR]

There are two contributions in this paper. The first is that the abstract result for the existence of the unique solution of certain nonlinear parabolic equation is obtained by using the properties of H-monotone operators, consequently, the proof is simplified compared to the corresponding discussions in the literature. The second is that the connections between resolvent of H-monotone operators and solutions of nonlinear parabolic equations are shown, and this strengthens the importance of H-monotone operators, which have already attracted the attention of mathematicians because of the connections with practical problems. [ABSTRACT FROM AUTHOR]

In this paper, the periodic and subharmonic solutions are investigated for a class of second-order non-autonomous ordinary differential equations with a p-Laplacian. With the perturbation technique and the dual least action principle, some existence results are given of solutions to the convex p-Laplacian systems. [ABSTRACT FROM AUTHOR]