Results 11 to 20 of about 218 (139)
Vitali convergence theorem and Palais-Smale condition
Differential and Integral Equations, 2002 Let \(N\geq 2\) and ...
Chen, Min-Chun +2 more
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Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type
Abstract and Applied Analysis, 2013 We prove a theorem on the existence and uniqueness of a solution as well as on a sensitivity (i.e., differentiable dependence of a solution on a functional parameter) of a fractional integrodifferential Cauchy problem of Volterra type.
Dariusz Idczak +2 more
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Journal of Functional Analysis, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A note on Palais-Smale condition and coercivity
Differential and Integral Equations, 1990 It has been observed [the second author, An existence theorem on multiple critical points and its applications in nonlinear P.D.E., in Differential geometry and differential equations, Proc. Symp., Changchun/China 1982, 479-483 (1986); the third author, An introduction to critical point theory (1988)] that, for a \(C^ 1\) function \(\varphi\) bounded ...
Čaklović, L., Li, Shu Jie, Willem, M.
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Curve-straightening and the Palais-Smale condition [PDF]
Transactions of the American Mathematical Society, 1998 This paper considers the negative gradient trajectories associated with the modified total squared curvature functional ∫
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New Periodic Solutions for the Singular Hamiltonian System
Abstract and Applied Analysis, 2014 By use of the Cerami-Palais-Smale condition, we generalize the classical Weierstrass minimizing theorem to the singular case by allowing functions which attain infinity at some values. As an application, we study certain singular second-order Hamiltonian
Yi Liao
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Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 13324-13360, August 2026.ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type −ΔΦ1u=Fu(x,u,v)+λRu(x,u,v)inΩ−ΔΦ2v=−Fv(x,u,v)−λRv(x,u,v)inΩu=v=0on∂Ω$$ \left\{\begin{array}{l}\hfill -{\Delta}_{\Phi_1}u={F}_u\left(x,u,v\right)+\lambda {R}_u\left(x,u,v\right)\kern0.1832424242424242em \mathrm{in}\kern0.3em \Omega ...
Lucas da Silva, Marco Souto
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Low eigenvalues of the p$p$–Laplacian in general open sets
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract We consider the minmax Ljusternik–Schnirelmann levels of the constrained p$p$–Dirichlet integral on a general open set of the Euclidean space. We show that, whenever one of these levels lies below the threshold given by the Lp$L^p$ Poincaré constant “at infinity,” it actually defines an eigenvalue of the Dirichlet p$p$–Laplacian. We also prove
Lorenzo Brasco +2 more
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Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media
Boundary Value Problems, 2005 We study nonlinear eigenvalue problems of the type −div(a(x)∇u)=g(λ,x,u) in â„ÂN, where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity ...
Vicenţiu RăDulescu +1 more
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Existence and multiplicity of solutions for a nonhomogeneous Neumann boundary problem [PDF]
Opuscula Mathematica, 2015 We consider a nonlinear Neumann elliptic equation driven by a \(p\)-Laplacian-type operator which is not homogeneous in general. For such an equation the energy functional does not need to be coercive, and we use suitable variational methods to show that
Liliana Klimczak
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