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Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.

Differential equations, Elliptic. --- Differential equations, Partial. --- Partial differential equations --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Dirichlet Problems for Elliptic Equations. --- Distributional Solution. --- Entropy Solutions. --- Leray-Lions Problem. --- Nonlinear Elliptic Partial Differential Equations in Divergence Form. --- Sobolev Space.

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This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Research & information: general --- Mathematics & science --- fourth-order differential equations --- neutral delay --- oscillation --- ψ-Caputo fractional derivative --- Cauchy problem extremal solutions --- monotone iterative technique --- upper and lower solutions --- third-order differential equation --- boundary value problem --- existence --- sign conditions --- mixed type nonlinear equation --- hilfer operator --- mittag–leffler function --- spectral parameter --- solvability --- equations of the pseudo-elliptic type of third order --- energy estimate --- analog of the Saint-Venant principle --- even-order differential equations --- Dirac delta function --- distributional solution --- Laplace transform --- power series solution --- integro-differential equation --- mixed type equation --- small parameter --- spectral parameters --- Caputo operators of different fractional orders --- inverse problem --- one value solvability --- Rosenzweig–MacArthur model --- fractional derivatives --- threshold harvesting --- distributed-order fractional calculus --- basic optimal control problem --- Pontryagin extremals --- fourth-order differential equations --- neutral delay --- oscillation --- ψ-Caputo fractional derivative --- Cauchy problem extremal solutions --- monotone iterative technique --- upper and lower solutions --- third-order differential equation --- boundary value problem --- existence --- sign conditions --- mixed type nonlinear equation --- hilfer operator --- mittag–leffler function --- spectral parameter --- solvability --- equations of the pseudo-elliptic type of third order --- energy estimate --- analog of the Saint-Venant principle --- even-order differential equations --- Dirac delta function --- distributional solution --- Laplace transform --- power series solution --- integro-differential equation --- mixed type equation --- small parameter --- spectral parameters --- Caputo operators of different fractional orders --- inverse problem --- one value solvability --- Rosenzweig–MacArthur model --- fractional derivatives --- threshold harvesting --- distributed-order fractional calculus --- basic optimal control problem --- Pontryagin extremals