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Publication The Gauss Image Problem(Wiley, 2020) Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong; Zhao, Yiming; Department of Mathematics and Its ApplicationsPublication Smoothness in the 𝐿𝑝 Minkowski Problem for 𝑝<1(Springer, 2020) Bianchi, Gabriele; Böröczky, Károly J.; Colesanti, Andrea; Department of Mathematics and Its ApplicationsWe discuss the smoothness and strict convexity of the solution of the L p-Minkowski problem when p < 1 and the given measure has a positive density function.Publication New competition phenomena in Dirichlet problems(2010) Kristály, Alexandru; Moroșanu, Gheorghe; Department of Mathematics and its ApplicationsWe study the multiplicity of nonnegative solutions to the problem, (Pλ) where Ω is a smooth bounded domain in RN, f:[0,∞)→R oscillates near the origin or at infinity, and p>0, λ∈R. While oscillatory right-hand sides usually produce infinitely many distinct solutions, an additional term involving up may alter the situation radically. Via a direct variational argument we fully describe this phenomenon, showing that the number of distinct non-trivial solutions to problem (Pλ) is strongly influenced by up and depends on λ whenever one of the following two cases holds: •p⩽1 and f oscillates near the origin; •p⩾1 and f oscillates at infinity (p may be critical or even supercritical). The coefficient a∈L∞(Ω) is allowed to change its sign, while its size is relevant only for the threshold value p=1 when the behaviour of f(s)/s plays a crucial role in both cases. Various - and L∞-norm estimates of solutions are also given.Publication Eigenvalue problems in anisotropic Orlicz–Sobolev spaces(Académie des Sciences, France, 2009) Mihailescu, Mihai; Moroșanu, Gheorghe; Rădulescu, Vicenţiu D.; Department of Mathematics and Its ApplicationsWe establish sufficient conditions for the existence of solutions to a class of nonlinear eigenvalue problems involving nonhomogeneous differential operators in Orlicz–Sobolev spaces.Publication Homoclinic solutions of a fourth-order travelling wave ODE(2007) Moroșanu, Gheorghe; Souroujon, Diko; Tersian, Stepan; Department of Mathematics and Its ApplicationsPublication Elliptic-like regularization of semilinear evolution equations(2012) Ahsan, Muhammad; Moroșanu, Gheorghe; Department of Mathematics and Its ApplicationsConsider in a real Hilbert space the Cauchy problem (P0): u′(t)+Au(t)+Bu(t) = f (t), 0 ≤ t ≤ T ; u(0) = u_0, where −A is the generator of a C_0-semigroup of linear contractions and B is a smooth nonlinear operator. We associate with (P_0) the following problem: (Pε): −εu′′(t) + u′(t) + Au(t) + Bu(t) = f (t), 0 ≤ t ≤ T ; u(0) = u_0, u(T ) = u_1, where ε > 0 is a small parameter. Existence, uniqueness and higher regularity for both (P0) and (Pε) are investigated and an asymptotic expansion for the solution of problem (Pε) is established, showing the presence of a boundary layer near t = T .Publication Eigenvalues of the Laplace operator with nonlinear boundary conditions(2011) Mihailescu, Mihai; Moroșanu, Gheorghe; Department of Mathematics and Its ApplicationsAn eigenvalue problem on a bounded domain for the Laplacian with a nonlinear Robin-like boundary condition is investigated. We prove the existence, isolation and simplicity of the first two eigenvalues.Publication Asymptotically periodic solutions for differential and difference inclusions in Hilbert spaces(Texas State University, 2013) Moroșanu, Gheorghe; Ozpinar, Figen; Department of Mathematics and Its Applications