weak solutions
Stability of weak solutions for the large scale atmospheric equations
... The rest of the paper is as follows. In Section , the main results about the L -stability of weak solutions to the Navier-Stokes equations and temperature equation are stated. In Section , we will give ...
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Existence and uniqueness of weak solutions for a class of fractional superdiffusion equations
... of weak solutions (or positive solutions) of fractional-order differential equations, our main aim is to develop the Schauder fixed point theorem and the Arzelà-Ascoli compactness theorem for solving a ...
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Existence of nontrivial weak solutions for a quasilinear Choquard equation
... of weak solutions for the problem above via the mountain pass theorem and the fountain ...of weak solutions to the problem near the origin under suitable assumptions for the nonlinear term f ...
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Existence of weak solutions for abstract hyperbolic parabolic equations
... In this is work he proved the existence of classical solution by iterative methods for the mixed problem associated to the equation... EXISTENCE OF WEAK SOLUTIONS FOR CAUCHY PROBLEMS.[r] ...
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Infinitely many weak solutions for a fractional Schrödinger equation
... In this paper we are concerned with the fractional Schrödinger equation (– ) α u + V(x)u = f (x,u), x ∈ R N , where 0 < α < 1, N > 2 α , (– ) α stands for the fractional Laplacian of order α , V is a positive ...
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Stability of weak solutions to obstacle problem in Clifford analysis
... This paper is organized as follows. In Section , some preliminary results about Clifford- valued functions are presented. In Section , higher integrability of weak solutions to ob- stacle problem for ...
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Relaxation and weak solutions of nonlocal semilinear evolution systems
... and weak solutions are defined and the relations between them are ...alized solutions for our system ...limit solutions may not be mild ...limit solutions are in fact weak ...
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Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces
... of weak noncompactness and Henstock-Kurzweil-Pettis integrals to discuss the existence theorem of weak solutions for a class of nonlinear fractional integrodifferential equations in a nonreflexive ...
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ON THE WEAK SOLUTIONS OF THE URYSOHN-STIELTJES FUNCTIONAL INTEGRAL EQUATIONS
... If x is weakly continuous on I , then x is strongly measurable and hence weakly measurable (see [14] and [10]). It is evident that in reflexive Banach spaces, if x is weakly continuous function on [a, b], then x is ...
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Existence of weak solutions for a class of quasilinear elliptic systems
... of weak solutions for problem () at resonance with the higher eigenvalues of problem ...of weak solutions for problem () by using variational methods, Morse theory and critical ...
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Convergence of very weak solutions to A Dirac equations in Clifford analysis
... very weak solutions to A-Dirac equations DA(x, Du) = 0 with Dirichlet boundary ...very weak solutions to A-Dirac equations is obtained in Clifford ...
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On weak solutions of the equations of motion of a viscoelastic medium with variable boundary
... a weak sense and application of the topological theory of a degree that allows to establish the existence of solutions on the basis of a priori estimates and statements about passage to the ...for ...
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Interpolation inequalities for weak solutions of nonlinear parabolic systems
... Key of this note is the use of interpolation theorems of Gagliardo-Nirenberg type. The use of interpolation theory, made in [9] and in [1] with montonicity assumption and quadratic growth, as illustrated in [10], has ...
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Remarks on weak solutions for a nonlocal parabolic problem
... of weak solutions for a diffusion prob- lem associated with nonlinear diffusions of nonlocal type studied by Chipot and Lovat (1999) by an application of the fixed point result of ...
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Local Boundedness of Weak Solutions for Nonlinear Parabolic Problem with Growth
... of weak solutions of parabolic equation with p-growth conditions, where p is a constant, for example 8, ...the weak solutions plays a central role in many ...
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Weak solutions of degenerated quasilinear elliptic equations of higher order
... We prove the existence of weak solutions of higher order degenerated quasihnear elliptic equations The mmn tools are the degree theory for generahzed monotone mappings and mbeddlng theor[r] ...
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Existence of Weak Solutions for a Nonlinear Elliptic System
... In Section 2, we introduce some notations and lemmas needed in later sections. In Section 3, we investigate the existence, uniqueness, stability, and continuity of solution p to the nonlinear equation 1.3. In Section 4, ...
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Weak solutions for the singular potential wave system
... of weak solutions for a class of the system of wave equations with singular potential ...nontrivial weak solution for a class of the wave system with singular potential nonlinearity and the Dirichlet ...
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Compatibility conditions for the existence of weak solutions to a singular elliptic equation
... When p = , the corresponding results are much fewer. By using a sub-supersolution approach and a mountain pass theorem, Giacomoni et al. [] proved, among other things, that when h(x) ≡ λ, k(x) ≡ , < α < and ...
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The investigation of local weak solutions for a generalized Novikov equation
... uniqueness of analytic solutions for Eq. () are obtained in []. It is worthy to mention that if the Sobolev index s ≥ and sign conditions hold, the orbit invariants are applied to show the existence of ...
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